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A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment
Shock and Vibration ( IF 1.6 ) Pub Date : 2021-06-17 , DOI: 10.1155/2021/1328886
Guohua Gao 1 , Ningze Sun 1 , Dong Shao 1, 2 , Yongqiang Tao 3 , Wei Wu 3
Affiliation  

This article mainly analyzes the free vibration characteristic of the sandwich piezoelectric beam under elastic boundary conditions and thermal environment. According to the first-order shear deformation theory and Hamilton’s principle, the thermo-electro-elastic coupling equations of the sandwich piezoelectric beam are obtained. Meanwhile, elastic boundary conditions composed of an array of springs are introduced, and the displacement variables and external potential energy of the beam are expressed as wave functions. By using the method of reverberation-ray matrix to integrate and solve the governing equations, a search algorithm based on golden-section search is introduced to calculate the required frequency parameters. A series of numerical results are compared with those reported in literature studies and obtained by simulation software to verify the correctness and versatility of the search algorithm. In addition, three parametric research cases are proposed to investigate the frequency parameters of sandwich piezoelectric beams with elastic restraint conditions, material parameters, thickness ratio, different temperature rises, and external electric potential.

中文翻译:

热环境下具有一般边界条件的夹层压电层合梁自由振动的统一分析

本文主要分析了弹性边界条件和热环境下夹层压电梁的自由振动特性。根据一阶剪切变形理论和哈密顿原理,得到了夹层压电梁的热电弹性耦合方程。同时引入了由一组弹簧组成的弹性边界条件,将梁的位移变量和外部势能表示为波函数。利用混响射线矩阵的方法对控制方程进行积分求解,引入了一种基于黄金分割搜索的搜索算法来计算所需的频率参数。将一系列数值结果与文献研究报告的数值结果进行比较,并通过仿真软件获得,以验证搜索算法的正确性和通用性。此外,提出了三个参数研究案例,研究了弹性约束条件、材料参数、厚度比、不同温升和外部电位的夹层压电梁的频率参数。
更新日期:2021-06-17
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