Solution of Special Mixed Dynamic Problems of Anisotropic Plates.
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| Title: | Solution of Special Mixed Dynamic Problems of Anisotropic Plates. |
|---|---|
| Alternate Title: | Անիզոտրոպ սալերի տարածական խառը դինամիկական խնդիրների լուծման մասին. К решению пространственных смешанных динамических задач анизотропных пластин. |
| Authors: | Aghalovyan, L. A.1 lagal@sci.am, Aghalovyan, M. L.2 mheraghalovyan@yahoo.com, Zakaryan, T. V.3 zaqaryantatevik@mail.ru, Tovmasyan, A. B.3 Tovmasyanarthur01@gmail.com |
| Source: | Proceedings of the National Academy of Sciences of Armenia. Mechanics. 2026, Vol. 79 Issue 1/2, p119-132. 14p. |
| Subjects: | Structural plates, Boundary value problems, Frequencies of oscillating systems, Shearing force, Oscillations, Displacement (Mechanics), Asymptotic expansions |
| Abstract (English): | Тhe spatial mixed dynamic problem for anisotropic plates is solved. It is assumed, that the plate has a plane of elastic symmetry, the facial surface is imparted normal displacements that change harmonically over time, and the shear stresses there are equal to zero. The lower facial surface of the plate is rigidly fixed. For this class of problems, the hypotheses of the classical and well-known refined theories of plates (Reissner E., Ambartsumyan S., Timoshenko’s type aren’t applicable. The asymptotic solution to the problem is obtained. It is shown that longitudinal oscillations in the vertical direction are dominant, which also generate tangential oscillations, the amplitudes of which, however, are an order of magnitude smaller than the longitudinal ones. The conditions for the occurrence of resonance were established and the values of resonant frequencies were determined. If the displacements subjected to the facial surface depend polynomially on the tangential coordinates, the solution becomes mathematically exact. The illustrative example is given. [ABSTRACT FROM AUTHOR] |
| Abstract (Russian): | Решена пространственная смешанная динамическая задача для анизотропных пластин. Считается, что пластина имеет плоскость упругой симметрии, лицевой поверхности сообщены нормальные перемещения гармонически изменяющиеся во времени, а касательные напряжения там равны нулю. Нижняя лицевая поверхность пластины жёстко закреплена. Для этого класса задач гипотезы классической и известных уточненных теорий пластин (Рейснер Е., Амбарцумян С., типа Тимошенко) неприменимы. Получено асимптотическое решение задачи. Показано, что доминирующими являются продольные колебания в вертикальном направлении, которые порождают также тангенциальные колебания, амплитуда которых, однако, на порядок меньше продольных. Установлены условия возникновения резонанса и определены значения резонансных частот. Если сообщаемые лицевой поверхности перемещения полиномиально зависят от тангенциальных координат, решение становится математически точным. Приведён иллюстрационный пример. [ABSTRACT FROM AUTHOR] |
| Copyright of Proceedings of the National Academy of Sciences of Armenia. Mechanics is the property of National Academy of Sciences of the Republic of Armenia 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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| Items | – Name: Title Label: Title Group: Ti Data: Solution of Special Mixed Dynamic Problems of Anisotropic Plates. – Name: TitleAlt Label: Alternate Title Group: TiAlt Data: Անիզոտրոպ սալերի տարածական խառը դինամիկական խնդիրների լուծման մասին.<br />К решению пространственных смешанных динамических задач анизотропных пластин. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Aghalovyan%2C+L%2E+A%2E%22">Aghalovyan, L. A.</searchLink><relatesTo>1</relatesTo><i> lagal@sci.am</i><br /><searchLink fieldCode="AR" term="%22Aghalovyan%2C+M%2E+L%2E%22">Aghalovyan, M. L.</searchLink><relatesTo>2</relatesTo><i> mheraghalovyan@yahoo.com</i><br /><searchLink fieldCode="AR" term="%22Zakaryan%2C+T%2E+V%2E%22">Zakaryan, T. V.</searchLink><relatesTo>3</relatesTo><i> zaqaryantatevik@mail.ru</i><br /><searchLink fieldCode="AR" term="%22Tovmasyan%2C+A%2E+B%2E%22">Tovmasyan, A. B.</searchLink><relatesTo>3</relatesTo><i> Tovmasyanarthur01@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+National+Academy+of+Sciences+of+Armenia%2E+Mechanics%22">Proceedings of the National Academy of Sciences of Armenia. Mechanics</searchLink>. 2026, Vol. 79 Issue 1/2, p119-132. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Structural+plates%22">Structural plates</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Frequencies+of+oscillating+systems%22">Frequencies of oscillating systems</searchLink><br /><searchLink fieldCode="DE" term="%22Shearing+force%22">Shearing force</searchLink><br /><searchLink fieldCode="DE" term="%22Oscillations%22">Oscillations</searchLink><br /><searchLink fieldCode="DE" term="%22Displacement+%28Mechanics%29%22">Displacement (Mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+expansions%22">Asymptotic expansions</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: Тhe spatial mixed dynamic problem for anisotropic plates is solved. It is assumed, that the plate has a plane of elastic symmetry, the facial surface is imparted normal displacements that change harmonically over time, and the shear stresses there are equal to zero. The lower facial surface of the plate is rigidly fixed. For this class of problems, the hypotheses of the classical and well-known refined theories of plates (Reissner E., Ambartsumyan S., Timoshenko’s type aren’t applicable. The asymptotic solution to the problem is obtained. It is shown that longitudinal oscillations in the vertical direction are dominant, which also generate tangential oscillations, the amplitudes of which, however, are an order of magnitude smaller than the longitudinal ones. The conditions for the occurrence of resonance were established and the values of resonant frequencies were determined. If the displacements subjected to the facial surface depend polynomially on the tangential coordinates, the solution becomes mathematically exact. The illustrative example is given. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Russian) Group: Ab Data: Решена пространственная смешанная динамическая задача для анизотропных пластин. Считается, что пластина имеет плоскость упругой симметрии, лицевой поверхности сообщены нормальные перемещения гармонически изменяющиеся во времени, а касательные напряжения там равны нулю. Нижняя лицевая поверхность пластины жёстко закреплена. Для этого класса задач гипотезы классической и известных уточненных теорий пластин (Рейснер Е., Амбарцумян С., типа Тимошенко) неприменимы. Получено асимптотическое решение задачи. Показано, что доминирующими являются продольные колебания в вертикальном направлении, которые порождают также тангенциальные колебания, амплитуда которых, однако, на порядок меньше продольных. Установлены условия возникновения резонанса и определены значения резонансных частот. Если сообщаемые лицевой поверхности перемещения полиномиально зависят от тангенциальных координат, решение становится математически точным. Приведён иллюстрационный пример. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Proceedings of the National Academy of Sciences of Armenia. Mechanics is the property of National Academy of Sciences of the Republic of Armenia 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: 10.54503/0002-3051-2026.79.1-2-119 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 119 Subjects: – SubjectFull: Structural plates Type: general – SubjectFull: Boundary value problems Type: general – SubjectFull: Frequencies of oscillating systems Type: general – SubjectFull: Shearing force Type: general – SubjectFull: Oscillations Type: general – SubjectFull: Displacement (Mechanics) Type: general – SubjectFull: Asymptotic expansions Type: general Titles: – TitleFull: Solution of Special Mixed Dynamic Problems of Anisotropic Plates. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Aghalovyan, L. A. – PersonEntity: Name: NameFull: Aghalovyan, M. L. – PersonEntity: Name: NameFull: Zakaryan, T. V. – PersonEntity: Name: NameFull: Tovmasyan, A. B. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00023051 Numbering: – Type: volume Value: 79 – Type: issue Value: 1/2 Titles: – TitleFull: Proceedings of the National Academy of Sciences of Armenia. Mechanics Type: main |
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