 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13653 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8223
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| In English (Mech. Solids): | | 5430 |
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| M.M. Zhang and E. Bai, "New Analytic Free Vibration Solutions of Free-Edge Orthotropic Moderately Thick Rectangular Plates by the Symplectic Superposition Method," Mech. Solids. 60 (8), 7110-7124 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
8 |
Pages |
7110-7124 |
| DOI |
10.1134/S0025654425605142 |
| Title |
New Analytic Free Vibration Solutions of Free-Edge Orthotropic Moderately Thick Rectangular Plates by the Symplectic Superposition Method |
| Author(s) |
M.M. Zhang (School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021 China)
E. Bai (School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021 China; Key Laboratory of Mathematical Modeling and Scientific Computing, Hohhot, 010021 China, ebu@imu.edu.cn) |
| Abstract |
The goal of this paper is to uniformly study the free vibration problems of free-edge (FFFF)
orthotropic/isotropic rectangular plates with different aspect ratios and thickness-to-width ratios
using the symplectic superposition method (SSM). The governing equations for the orthotropic moderately thick rectangular plate (MTRP) are first transformed into Hamiltonian canonical equations.
Then, by analyzing the boundary conditions (BCs) of the plate, the vibration problem of the original
FFFF orthotropic MTRP is decomposed into two sub-vibration problems with sliding supports on
two opposite sides. After that, the general solutions for these two sub-vibration problems are obtained
using the separation of variables method in the Hamiltonian framework. Then, based on the superposition method, the symplectic superposition solution for the original vibration problem is derived by
superimposing the general solutions of these two sub-vibration problems. In examples, the symplectic
superposition solution is applied to present the vibration frequencies and corresponding modes for
orthotropic rectangular plates with different thickness-to-width ratios and aspect ratios. Additionally,
the change rules of vibration frequencies with aspect ratios, thickness-to-width ratios, and elastic
modulus ratios are analyzed. The SSM does not need to set any trial function in advance, its solving
process can be achieved through step-by-step rigorous derivation, and this method has a wide range of
applications. For example, this method can be used to study the buckling and vibration of plates with
different materials and shapes under more complex boundary conditions. |
| Keywords |
moderately thick rectangular plate, Hamiltonian canonical equations, vibration problem, variable separation method, symplectic superposition method |
| Received |
19 September 2025 | Revised |
28 November 2025 | Accepted |
01 December 2025 |
| Link to Fulltext |
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