 | | 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: | | 13427 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8178
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| In English (Mech. Solids): | | 5249 |
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| X. Su, J. L. Zhang, T. Li, J.B. Sun, X.S. Xu, and Z.H. Zhou, "A Novel Analytical Model for Free Vibration of Irregular Stepped Orthotropic Cantilevered Plates," Mech. Solids. 60 (6), 5435-5478 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
6 |
Pages |
5435-5478 |
| DOI |
10.1134/S0025654425604045 |
| Title |
A Novel Analytical Model for Free Vibration of Irregular Stepped Orthotropic Cantilevered Plates |
| Author(s) |
X. Su (State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, 116024 China)
J. L. Zhang (State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, 116024 China)
T. Li (State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, 116024 China)
J.B. Sun (State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Chemical Engineering Ocean and Life Science, Dalian University of Technology, Panjin, 124221 China)
X.S. Xu (State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, 116024 China)
Z.H. Zhou (State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian, 116024 China, zhouzh@dlut.edu.cn) |
| Abstract |
Multi-level thickness irregular plates have garnered widespread applications in diverse engineering fields, driven by the growing demands for lightweight structural designs, enhanced strength
capabilities, and the reduction of welding necessities. In this paper, analytical solutions for free vibration of irregular stepped orthotropic cantilevered plates (SOCPs), including L-shaped, T-shaped,
Z-shaped, and cross-sharped plates, are derived within the framework of symplectic mechanics. The
overall SOCP is regarded as a combination of multiple uniform-thickness rectangular plates, thereby
its analytical solutions can be obtained by using the symplectic method and a boundary superposition
technique. Therefore, accurate natural frequencies and analytical vibration mode shapes are obtained
simultaneously. The derivation procedure is conducted in a step-by-step manner, ensuring each stage
is accompanied by a rigorous definition and logical progression. In numerical examples, a comparison
study is first given. The present results are compared with those reported in the literature and computed by finite element method, and excellent agreements are observed. Furthermore, the effects of
cantilever boundary conditions and thickness ratios on the vibration characteristics of the L-shaped,
T-shaped, Z-shaped, and cross-sharped plates are investigated and discussed in detail. The obtained
natural frequencies and analytical vibration mode shapes of these irregular SOCPs can be served as
benchmarks for future approximate and numerical methods. |
| Keywords |
symplectic method, irregular plate, stepped thickness, free vibration, analytical solution |
| Received |
28 July 2025 | Revised |
19 September 2025 | Accepted |
22 September 2025 |
| Link to Fulltext |
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