Applied Mathematics and Mechanics >
New analytical solutions for free vibration of embedded magneto-electro-elastic cylindrical shells with step-wise thickness variations
Received date: 2024-11-02
Revised date: 2025-01-09
Online published: 2025-03-03
Supported by
Project supported by the Science and Technology Plan Joint Program of Liaoning Province of China (Natural Science Foundation-Doctoral Research Launch Project) (No. 2024-BSLH-027), the Fundamental Research Funds for Undergraduate Universities of Liaoning Province of China (No. LJBKY2024033), the National Natural Science Foundation of China (No. 12472064), and the Natural Science Foundation of Liaoning Province of China (No. 2023-MS-118)
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In recent years, magneto-electro-elastic (MEE) cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting. To aid the design of such energy harvesting devices, an accurate free vibration analysis of embedded MEE cylindrical shells with step-wise thicknesses is performed within the framework of symplectic mechanics. By using the Legendre transformation, a new known vector is defined to transform the higher-order partial differential governing equations into a set of lower-order ordinary differential equations. Therefore, the original vibration analysis is regarded as an eigen problem in the symplectic space, and analytical solutions can be represented by the symplectic series. In numerical examples, the new analytical solutions are compared with the existing results, and good agreement is observed. Furthermore, the effects of critical design parameters on free vibration characteristics are thoroughly investigated. All numerical results can serve as benchmarks for the development of other approximate or numerical methods.
Jufang JIA, Huilin YIN, Qinyu YU, Jiabin SUN, Xinsheng XU, Zhenhuan ZHOU . New analytical solutions for free vibration of embedded magneto-electro-elastic cylindrical shells with step-wise thickness variations[J]. Applied Mathematics and Mechanics, 2025 , 46(3) : 447 -466 . DOI: 10.1007/s10483-025-3228-7
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