Free vibrations of shallow-spherical shells on fractional-order viscoelastic foundations.
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| Title: | Free vibrations of shallow-spherical shells on fractional-order viscoelastic foundations. |
|---|---|
| Authors: | Liu, Wenwu1 (AUTHOR), Meng, Xiangyun1 (AUTHOR), Zhou, Xiaoli1,2 (AUTHOR) zhouxiaoli@hebeu.edu.cn, Wei, Peijun2,3 (AUTHOR) weipj@ustb.edu.cn |
| Source: | Acta Mechanica. Nov2025, Vol. 236 Issue 11, p6789-6803. 15p. |
| Subjects: | Free vibration, Spherical shells (Engineering), Numerical analysis, Bessel functions, Eigenfrequencies, Viscoelasticity, Mechanical vibration research |
| Abstract: | The free vibration characteristics of a shallow-spherical shell mounted on the viscoelastic foundation which is characterized by the fractional-order Maxwell model is studied. Firstly, the fractional-order Maxwell viscoelastic model of foundation is introduced, this model is applicable to engineering scenarios where the foundation exhibits significant viscoelastic behavior, such as the clay stratum and liquid saturated porous stratum, and the frequency-dependent complex modulus and the reaction force resulted from foundation are given. Then, with the help of the stress function, the governing differential equations of the shallow-spherical shell mounted on the viscoelastic foundation are derived in term of only the stress function and the transversal displacement. The complete analytic solution of the stress function and the transversal displacement are finally obtained in term of the classical Bessel functions and the modified Bessel functions. The complex natural frequency is introduced to reflect the attenuation feature of the free vibration. Finally, the numerical example is provided for shallow-spherical shell with the fixed-edge boundary conditions. The first three orders of natural frequencies and the vibration pattern and the corresponding attenuation index are estimated and shown in tables and 3D cloud figure. The influences of the viscoelastic foundation and the two typical vibration patterns with the axisymmetric and the non-axisymmetric properties are discussed in detail. [ABSTRACT FROM AUTHOR] |
| Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 189253797 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Free vibrations of shallow-spherical shells on fractional-order viscoelastic foundations. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Liu%2C+Wenwu%22">Liu, Wenwu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Meng%2C+Xiangyun%22">Meng, Xiangyun</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhou%2C+Xiaoli%22">Zhou, Xiaoli</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> zhouxiaoli@hebeu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wei%2C+Peijun%22">Wei, Peijun</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> weipj@ustb.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Acta+Mechanica%22">Acta Mechanica</searchLink>. Nov2025, Vol. 236 Issue 11, p6789-6803. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Free+vibration%22">Free vibration</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+shells+%28Engineering%29%22">Spherical shells (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Bessel+functions%22">Bessel functions</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfrequencies%22">Eigenfrequencies</searchLink><br /><searchLink fieldCode="DE" term="%22Viscoelasticity%22">Viscoelasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+vibration+research%22">Mechanical vibration research</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The free vibration characteristics of a shallow-spherical shell mounted on the viscoelastic foundation which is characterized by the fractional-order Maxwell model is studied. Firstly, the fractional-order Maxwell viscoelastic model of foundation is introduced, this model is applicable to engineering scenarios where the foundation exhibits significant viscoelastic behavior, such as the clay stratum and liquid saturated porous stratum, and the frequency-dependent complex modulus and the reaction force resulted from foundation are given. Then, with the help of the stress function, the governing differential equations of the shallow-spherical shell mounted on the viscoelastic foundation are derived in term of only the stress function and the transversal displacement. The complete analytic solution of the stress function and the transversal displacement are finally obtained in term of the classical Bessel functions and the modified Bessel functions. The complex natural frequency is introduced to reflect the attenuation feature of the free vibration. Finally, the numerical example is provided for shallow-spherical shell with the fixed-edge boundary conditions. The first three orders of natural frequencies and the vibration pattern and the corresponding attenuation index are estimated and shown in tables and 3D cloud figure. The influences of the viscoelastic foundation and the two typical vibration patterns with the axisymmetric and the non-axisymmetric properties are discussed in detail. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00707-025-04487-3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 6789 Subjects: – SubjectFull: Free vibration Type: general – SubjectFull: Spherical shells (Engineering) Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Bessel functions Type: general – SubjectFull: Eigenfrequencies Type: general – SubjectFull: Viscoelasticity Type: general – SubjectFull: Mechanical vibration research Type: general Titles: – TitleFull: Free vibrations of shallow-spherical shells on fractional-order viscoelastic foundations. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Liu, Wenwu – PersonEntity: Name: NameFull: Meng, Xiangyun – PersonEntity: Name: NameFull: Zhou, Xiaoli – PersonEntity: Name: NameFull: Wei, Peijun IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00015970 Numbering: – Type: volume Value: 236 – Type: issue Value: 11 Titles: – TitleFull: Acta Mechanica Type: main |
| ResultId | 1 |
