Rayleigh–Ritz Approximation of the Acoustic Vibrations of Clamped Superquadrics—Application to Free Core–Shell Objects.
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| Title: | Rayleigh–Ritz Approximation of the Acoustic Vibrations of Clamped Superquadrics—Application to Free Core–Shell Objects. |
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| Authors: | S, Sajana1 (AUTHOR), Marco de Lucas, María del Carmen1 (AUTHOR), Saviot, Lucien1 (AUTHOR) lucien.saviot@cnrs.fr |
| Source: | Nanomaterials (2079-4991). Dec2025, Vol. 15 Issue 24, p1865. 10p. |
| Subjects: | Acoustic vibrations, Rayleigh-Ritz method, Isotropic properties, Numerical analysis, Symmetry, Solid geometry, Composite materials |
| Abstract: | A numerical approach based on the Rayleigh-Ritz method and using a modification of the so-called x y z algorithm is introduced to calculate the acoustic vibrations of clamped objects whose shape is delimited by superquadrics. It is then used to improve the convergence for the free vibrations of core–shell objects. The issue in this case is first illustrated in the simpler one-dimensional case of the thickness breathing vibration of an infinite "core-shell" plate. Functions suitable for solving the clamped vibrations of the core are added to the original x y z basis of functions to improve the convergence for core–shell superquadrics. The new basis obeys the same symmetry rules as the original one, which allows calculating vibrations for individual irreducible representations when the objects are made of cubic, tetragonal, or orthorhombic materials whose principal axes are aligned with those of the superquadrics. This method is validated for an isotropic spherical core–shell system for which analytic solutions exist. [ABSTRACT FROM AUTHOR] |
| Copyright of Nanomaterials (2079-4991) is the property of MDPI 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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 190528538 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Rayleigh–Ritz Approximation of the Acoustic Vibrations of Clamped Superquadrics—Application to Free Core–Shell Objects. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22S%2C+Sajana%22">S, Sajana</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Marco+de+Lucas%2C+María+del+Carmen%22">Marco de Lucas, María del Carmen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Saviot%2C+Lucien%22">Saviot, Lucien</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lucien.saviot@cnrs.fr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Nanomaterials+%282079-4991%29%22">Nanomaterials (2079-4991)</searchLink>. Dec2025, Vol. 15 Issue 24, p1865. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Acoustic+vibrations%22">Acoustic vibrations</searchLink><br /><searchLink fieldCode="DE" term="%22Rayleigh-Ritz+method%22">Rayleigh-Ritz method</searchLink><br /><searchLink fieldCode="DE" term="%22Isotropic+properties%22">Isotropic properties</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry%22">Symmetry</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+geometry%22">Solid geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Composite+materials%22">Composite materials</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A numerical approach based on the Rayleigh-Ritz method and using a modification of the so-called x y z algorithm is introduced to calculate the acoustic vibrations of clamped objects whose shape is delimited by superquadrics. It is then used to improve the convergence for the free vibrations of core–shell objects. The issue in this case is first illustrated in the simpler one-dimensional case of the thickness breathing vibration of an infinite "core-shell" plate. Functions suitable for solving the clamped vibrations of the core are added to the original x y z basis of functions to improve the convergence for core–shell superquadrics. The new basis obeys the same symmetry rules as the original one, which allows calculating vibrations for individual irreducible representations when the objects are made of cubic, tetragonal, or orthorhombic materials whose principal axes are aligned with those of the superquadrics. This method is validated for an isotropic spherical core–shell system for which analytic solutions exist. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Nanomaterials (2079-4991) is the property of MDPI 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190528538 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3390/nano15241865 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 1865 Subjects: – SubjectFull: Acoustic vibrations Type: general – SubjectFull: Rayleigh-Ritz method Type: general – SubjectFull: Isotropic properties Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Symmetry Type: general – SubjectFull: Solid geometry Type: general – SubjectFull: Composite materials Type: general Titles: – TitleFull: Rayleigh–Ritz Approximation of the Acoustic Vibrations of Clamped Superquadrics—Application to Free Core–Shell Objects. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: S, Sajana – PersonEntity: Name: NameFull: Marco de Lucas, María del Carmen – PersonEntity: Name: NameFull: Saviot, Lucien IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 12 Text: Dec2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 20794991 Numbering: – Type: volume Value: 15 – Type: issue Value: 24 Titles: – TitleFull: Nanomaterials (2079-4991) Type: main |
| ResultId | 1 |
