Solution of Special Mixed Dynamic Problems of Anisotropic Plates.
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| Title: | Solution of Special Mixed Dynamic Problems of Anisotropic Plates. |
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| 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] |
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| Database: | Engineering Source |
| Abstract: | 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] |
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| ISSN: | 00023051 |
| DOI: | 10.54503/0002-3051-2026.79.1-2-119 |
