GET https://dev.normadoc.fr/_partial/taxons/by-channel-menu-taxon/?template=%40SyliusShop%2FTaxon%2F_horizontalMenu.html.twig

Response
200 OK
IP
216.73.216.2
Profiled on
Token
42bbae

Components

3 Twig Components
11 Render Count
5 ms Render Time
156.0 MiB Memory Usage

Components

Name Metadata Render Count Render Time
ProductState 
"App\Twig\Components\ProductState"
components/ProductState.html.twig 		5 1.11ms
ProductMostRecent 
"App\Twig\Components\ProductMostRecent"
components/ProductMostRecent.html.twig 		5 3.65ms
ProductType 
"App\Twig\Components\ProductType"
components/ProductType.html.twig 		1 0.21ms

Render calls

ProductState App\Twig\Components\ProductState 156.0 MiB 0.30 ms
Input props 
[
  "product" => App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
  "showFullLabel" => "true"
]
Attributes 
[
  "showFullLabel" => "true"
]
Component 
App\Twig\Components\ProductState {#93007
  +product: App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
  +appearance: "state-withdrawn"
  +labels: [
    "Withdrawn"
  ]
  -stateAttributeCode: "state"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductType App\Twig\Components\ProductType 156.0 MiB 0.21 ms
Input props 
[
  "product" => App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
]
Attributes 
[]
Component 
App\Twig\Components\ProductType {#93187
  +product: App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
  +label: "Standard"
  -typeAttributeCode: "type"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductMostRecent App\Twig\Components\ProductMostRecent 156.0 MiB 0.72 ms
Input props 
[
  "product" => App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
]
Attributes 
[]
Component 
App\Twig\Components\ProductMostRecent {#93262
  +product: App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
  +label: "Most Recent"
  +icon: "check-xs"
  -mostRecentAttributeCode: "most_recent"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductState App\Twig\Components\ProductState 156.0 MiB 0.21 ms
Input props 
[
  "product" => App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
  "showFullLabel" => "true"
]
Attributes 
[
  "showFullLabel" => "true"
]
Component 
App\Twig\Components\ProductState {#106829
  +product: App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
  +appearance: "state-suspended"
  +labels: [
    "Superseded"
  ]
  -stateAttributeCode: "state"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductMostRecent App\Twig\Components\ProductMostRecent 156.0 MiB 0.77 ms
Input props 
[
  "product" => App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
]
Attributes 
[]
Component 
App\Twig\Components\ProductMostRecent {#106896
  +product: App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
  +label: "Historical"
  +icon: "historical"
  -mostRecentAttributeCode: "most_recent"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductState App\Twig\Components\ProductState 156.0 MiB 0.20 ms
Input props 
[
  "product" => App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
  "showFullLabel" => "true"
]
Attributes 
[
  "showFullLabel" => "true"
]
Component 
App\Twig\Components\ProductState {#113517
  +product: App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
  +appearance: "state-suspended"
  +labels: [
    "Superseded"
  ]
  -stateAttributeCode: "state"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductMostRecent App\Twig\Components\ProductMostRecent 156.0 MiB 0.72 ms
Input props 
[
  "product" => App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
]
Attributes 
[]
Component 
App\Twig\Components\ProductMostRecent {#113559
  +product: App\Entity\Product\Product {#106775
    #id: 8371
    #code: "IEEE00000356"
    #attributes: Doctrine\ORM\PersistentCollection {#106756 …}
    #variants: Doctrine\ORM\PersistentCollection {#106753 …}
    #options: Doctrine\ORM\PersistentCollection {#106749 …}
    #associations: Doctrine\ORM\PersistentCollection {#106751 …}
    #createdAt: DateTime @1751037361 {#106782
      date: 2025-06-27 17:16:01.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1754606304 {#106755
      date: 2025-08-08 00:38:24.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#106766 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#106793
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#106775}
        #id: 28493
        #name: "IEEE 176:1987"
        #slug: "ieee-176-1987-ieee00000356-240023"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          Withdrawn Standard. No abstract.<br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section , all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields. Real materials involve mechanical and electrical dissipation. In addition, they may show strong nonlinear behavior, hysteresis effects, temporal instability (aging), and a variety of magneto-mechano-electric interactions. For example, poled ferroelectric ceramics, commonly called piezoelectric ceramics, are a class of materials of major importance in commercial applications; yet because of the presence of ferroelectric domains, they exhibit a variety of nonlinearities and aging effects which are not within the scope of this standard. Although this standard does not treat nonlinear or aging effects in ceramics, it does present the equations commonly used to determine the piezoelectric properties of poled ceramic materials and uses the elastoelectric matrices of the equivalent crystal class (6mm) in a number of examples. It is not possible to state concisely a specific set of conditions under which the definitions and equations contained in this standard apply. In many cases of practical interest mechanical dissipation is the most important limitation on the validity of an analysis carried out for an ideal piezoelectric material. ANSI/IEEE Std 177-1966 [5] discusses in detail the electrical characteristics of resonators made of materials with mechanical losses and the simple equivalent circuit that can be used to represent these resonators in a frequency range near fundamental resonance. Section of this standard also provides discussion of the bounds imposed on the application of this standard to real materials. In brief, measurements based on this standard will be most meaningful when they are carried out on piezoelectric materials with small dissipations and negligible nonlinearities, like single-crystal dielectric solids or high-coupling-factor ceramics.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard on Piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#106764 …}
    #channels: Doctrine\ORM\PersistentCollection {#106758 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#106762 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#106760 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#106773 …}
    -apiLastModifiedAt: DateTime @1754517600 {#106742
      date: 2025-08-07 00:00:00.0 Europe/Paris (+02:00)
    }
    -lastUpdatedAt: DateTime @1704927600 {#106781
      date: 2024-01-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @570409200 {#106780
      date: 1988-01-29 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: DateTime @952297200 {#106774
      date: 2000-03-06 00:00:00.0 Europe/Paris (+01:00)
    }
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 74
    -documents: Doctrine\ORM\PersistentCollection {#106771 …}
    -favorites: Doctrine\ORM\PersistentCollection {#106769 …}
  }
  +label: "Historical"
  +icon: "historical"
  -mostRecentAttributeCode: "most_recent"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductState App\Twig\Components\ProductState 156.0 MiB 0.18 ms
Input props 
[
  "product" => App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
  "showFullLabel" => "true"
]
Attributes 
[
  "showFullLabel" => "true"
]
Component 
App\Twig\Components\ProductState {#113624
  +product: App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
  +appearance: "state-withdrawn"
  +labels: [
    "Withdrawn"
  ]
  -stateAttributeCode: "state"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductMostRecent App\Twig\Components\ProductMostRecent 156.0 MiB 0.72 ms
Input props 
[
  "product" => App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
]
Attributes 
[]
Component 
App\Twig\Components\ProductMostRecent {#113651
  +product: App\Entity\Product\Product {#7310
    #id: 11557
    #code: "IEEE00006315"
    #attributes: Doctrine\ORM\PersistentCollection {#7700 …}
    #variants: Doctrine\ORM\PersistentCollection {#7743 …}
    #options: Doctrine\ORM\PersistentCollection {#7915 …}
    #associations: Doctrine\ORM\PersistentCollection {#7899 …}
    #createdAt: DateTime @1751039788 {#7274
      date: 2025-06-27 17:56:28.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#7322
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#7921 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#7920
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#7310}
        #id: 41237
        #name: "ANSI/IEEE 176:1978"
        #slug: "ansi-ieee-176-1978-ieee00006315-243209"
        #description: """
          Revision Standard - Inactive-Withdrawn.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          This standard on piezoelectricity contains many equations based upon the analysis of vibrations in piezoelectric materials having simple geometrical shapes. Mechanical and electrical dissipation are never introduced into the theoretical treatment, and except for a brief discussion of nonlinear effects in Section 5, all the results are based on linear piezoelectricity in which the elastic, piezoelectric, and dielectric coefficients are treated as constants independent of the magnitude and frequency of applied mechanical stresses and electric fields.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standard On piezoelectricity"
        -notes: "Inactive-Withdrawn"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#7533 …}
    #channels: Doctrine\ORM\PersistentCollection {#7627 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#7612 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#7644 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#7389 …}
    -apiLastModifiedAt: DateTime @1743289200 {#7317
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1583881200 {#7292
      date: 2020-03-11 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @275868000 {#7318
      date: 1978-09-29 00:00:00.0 Europe/Paris (+02:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 58
    -documents: Doctrine\ORM\PersistentCollection {#7464 …}
    -favorites: Doctrine\ORM\PersistentCollection {#7499 …}
  }
  +label: "Most Recent"
  +icon: "check-xs"
  -mostRecentAttributeCode: "most_recent"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductState App\Twig\Components\ProductState 156.0 MiB 0.21 ms
Input props 
[
  "product" => App\Entity\Product\Product {#113452
    #id: 11556
    #code: "IEEE00006314"
    #attributes: Doctrine\ORM\PersistentCollection {#113486 …}
    #variants: Doctrine\ORM\PersistentCollection {#113488 …}
    #options: Doctrine\ORM\PersistentCollection {#113492 …}
    #associations: Doctrine\ORM\PersistentCollection {#113490 …}
    #createdAt: DateTime @1751039787 {#113459
      date: 2025-06-27 17:56:27.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#113461
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#113476 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#113717
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#113452}
        #id: 41233
        #name: "IEEE 176:1949"
        #slug: "ieee-176-1949-ieee00006314-243208"
        #description: """
           - Superseded.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          In 1945 a report entitled Standards on Piezoelectric Crystals: Recommended Terminologyn was prepared by the Committee on Piezoelectric Crystals and issued by the Institute. The present report involves not only much new material, but also a revision of certain portions of the earlier report. Part I of the 1945 report (corresponding to Part 1 of this Standard) remains unchanged, with the following exceptions: The use of left-handed axes for left crystals is now abandoned (see Sections 1,9, and 1.11 to 1.14); and the 1945 rules for rotated plates are now supplanted by the rules in the present report.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standards on Piezoelectric Crystals, 1949"
        -notes: "Superseded"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#113478 …}
    #channels: Doctrine\ORM\PersistentCollection {#113484 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#113480 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#113482 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#113469 …}
    -apiLastModifiedAt: DateTime @1743289200 {#113463
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1578006000 {#113464
      date: 2020-01-03 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @-632883600 {#113470
      date: 1949-12-12 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 20
    -documents: Doctrine\ORM\PersistentCollection {#113472 …}
    -favorites: Doctrine\ORM\PersistentCollection {#113474 …}
  }
  "showFullLabel" => "true"
]
Attributes 
[
  "showFullLabel" => "true"
]
Component 
App\Twig\Components\ProductState {#113732
  +product: App\Entity\Product\Product {#113452
    #id: 11556
    #code: "IEEE00006314"
    #attributes: Doctrine\ORM\PersistentCollection {#113486 …}
    #variants: Doctrine\ORM\PersistentCollection {#113488 …}
    #options: Doctrine\ORM\PersistentCollection {#113492 …}
    #associations: Doctrine\ORM\PersistentCollection {#113490 …}
    #createdAt: DateTime @1751039787 {#113459
      date: 2025-06-27 17:56:27.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#113461
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#113476 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#113717
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#113452}
        #id: 41233
        #name: "IEEE 176:1949"
        #slug: "ieee-176-1949-ieee00006314-243208"
        #description: """
           - Superseded.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          In 1945 a report entitled Standards on Piezoelectric Crystals: Recommended Terminologyn was prepared by the Committee on Piezoelectric Crystals and issued by the Institute. The present report involves not only much new material, but also a revision of certain portions of the earlier report. Part I of the 1945 report (corresponding to Part 1 of this Standard) remains unchanged, with the following exceptions: The use of left-handed axes for left crystals is now abandoned (see Sections 1,9, and 1.11 to 1.14); and the 1945 rules for rotated plates are now supplanted by the rules in the present report.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standards on Piezoelectric Crystals, 1949"
        -notes: "Superseded"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#113478 …}
    #channels: Doctrine\ORM\PersistentCollection {#113484 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#113480 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#113482 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#113469 …}
    -apiLastModifiedAt: DateTime @1743289200 {#113463
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1578006000 {#113464
      date: 2020-01-03 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @-632883600 {#113470
      date: 1949-12-12 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 20
    -documents: Doctrine\ORM\PersistentCollection {#113472 …}
    -favorites: Doctrine\ORM\PersistentCollection {#113474 …}
  }
  +appearance: "state-suspended"
  +labels: [
    "Superseded"
  ]
  -stateAttributeCode: "state"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}
ProductMostRecent App\Twig\Components\ProductMostRecent 156.0 MiB 0.73 ms
Input props 
[
  "product" => App\Entity\Product\Product {#113452
    #id: 11556
    #code: "IEEE00006314"
    #attributes: Doctrine\ORM\PersistentCollection {#113486 …}
    #variants: Doctrine\ORM\PersistentCollection {#113488 …}
    #options: Doctrine\ORM\PersistentCollection {#113492 …}
    #associations: Doctrine\ORM\PersistentCollection {#113490 …}
    #createdAt: DateTime @1751039787 {#113459
      date: 2025-06-27 17:56:27.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#113461
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#113476 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#113717
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#113452}
        #id: 41233
        #name: "IEEE 176:1949"
        #slug: "ieee-176-1949-ieee00006314-243208"
        #description: """
           - Superseded.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          In 1945 a report entitled Standards on Piezoelectric Crystals: Recommended Terminologyn was prepared by the Committee on Piezoelectric Crystals and issued by the Institute. The present report involves not only much new material, but also a revision of certain portions of the earlier report. Part I of the 1945 report (corresponding to Part 1 of this Standard) remains unchanged, with the following exceptions: The use of left-handed axes for left crystals is now abandoned (see Sections 1,9, and 1.11 to 1.14); and the 1945 rules for rotated plates are now supplanted by the rules in the present report.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standards on Piezoelectric Crystals, 1949"
        -notes: "Superseded"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#113478 …}
    #channels: Doctrine\ORM\PersistentCollection {#113484 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#113480 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#113482 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#113469 …}
    -apiLastModifiedAt: DateTime @1743289200 {#113463
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1578006000 {#113464
      date: 2020-01-03 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @-632883600 {#113470
      date: 1949-12-12 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 20
    -documents: Doctrine\ORM\PersistentCollection {#113472 …}
    -favorites: Doctrine\ORM\PersistentCollection {#113474 …}
  }
]
Attributes 
[]
Component 
App\Twig\Components\ProductMostRecent {#113784
  +product: App\Entity\Product\Product {#113452
    #id: 11556
    #code: "IEEE00006314"
    #attributes: Doctrine\ORM\PersistentCollection {#113486 …}
    #variants: Doctrine\ORM\PersistentCollection {#113488 …}
    #options: Doctrine\ORM\PersistentCollection {#113492 …}
    #associations: Doctrine\ORM\PersistentCollection {#113490 …}
    #createdAt: DateTime @1751039787 {#113459
      date: 2025-06-27 17:56:27.0 Europe/Paris (+02:00)
    }
    #updatedAt: DateTime @1753970307 {#113461
      date: 2025-07-31 15:58:27.0 Europe/Paris (+02:00)
    }
    #enabled: true
    #translations: Doctrine\ORM\PersistentCollection {#113476 …}
    #translationsCache: [
      "en_US" => App\Entity\Product\ProductTranslation {#113717
        #locale: "en_US"
        #translatable: App\Entity\Product\Product {#113452}
        #id: 41233
        #name: "IEEE 176:1949"
        #slug: "ieee-176-1949-ieee00006314-243208"
        #description: """
           - Superseded.<br />\n
          <br />\n
          \t\t\t\t<br />\n
          In 1945 a report entitled Standards on Piezoelectric Crystals: Recommended Terminologyn was prepared by the Committee on Piezoelectric Crystals and issued by the Institute. The present report involves not only much new material, but also a revision of certain portions of the earlier report. Part I of the 1945 report (corresponding to Part 1 of this Standard) remains unchanged, with the following exceptions: The use of left-handed axes for left crystals is now abandoned (see Sections 1,9, and 1.11 to 1.14); and the 1945 rules for rotated plates are now supplanted by the rules in the present report.
          """
        #metaKeywords: null
        #metaDescription: null
        #shortDescription: "IEEE Standards on Piezoelectric Crystals, 1949"
        -notes: "Superseded"
      }
    ]
    #currentLocale: "en_US"
    #currentTranslation: null
    #fallbackLocale: "en_US"
    #variantSelectionMethod: "match"
    #productTaxons: Doctrine\ORM\PersistentCollection {#113478 …}
    #channels: Doctrine\ORM\PersistentCollection {#113484 …}
    #mainTaxon: Proxies\__CG__\App\Entity\Taxonomy\Taxon {#7311 …}
    #reviews: Doctrine\ORM\PersistentCollection {#113480 …}
    #averageRating: 0.0
    #images: Doctrine\ORM\PersistentCollection {#113482 …}
    -supplier: Proxies\__CG__\App\Entity\Supplier\Supplier {#7325 …}
    -subscriptionCollections: Doctrine\ORM\PersistentCollection {#113469 …}
    -apiLastModifiedAt: DateTime @1743289200 {#113463
      date: 2025-03-30 00:00:00.0 Europe/Paris (+01:00)
    }
    -lastUpdatedAt: DateTime @1578006000 {#113464
      date: 2020-01-03 00:00:00.0 Europe/Paris (+01:00)
    }
    -author: ""
    -publishedAt: DateTime @-632883600 {#113470
      date: 1949-12-12 00:00:00.0 Europe/Paris (+01:00)
    }
    -releasedAt: null
    -confirmedAt: null
    -canceledAt: null
    -edition: null
    -coreDocument: "176"
    -bookCollection: ""
    -pageCount: 20
    -documents: Doctrine\ORM\PersistentCollection {#113472 …}
    -favorites: Doctrine\ORM\PersistentCollection {#113474 …}
  }
  +label: "Historical"
  +icon: "historical"
  -mostRecentAttributeCode: "most_recent"
  -localeContext: Sylius\Component\Locale\Context\CompositeLocaleContext {#1833 …}
}