层压压电板的等效单层 Mindlin 理论及其应用

MengMeng Lian, CuiYing Fan, GuoShuai Qin, Bingbing Wang, Chunsheng Lu, Ming-gao Zhao
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引用次数: 0

摘要

本文基于 Mindlin 一阶剪切变形理论,提出了等效单层 (ESL) 板理论来分析层压压电板 (LPP) 的机电耦合问题。该方法的主要特点是(i) 假设厚度上的电动势为多项式函数,确保其在界面上的连续性。(ii) 电位移在界面上是连续的,符合层压板之间的界面连续性条件。得出了 LPP 的变形和电动势的理论解。通过与三维有限元法(FEM)得到的两层和四层 LPP 的结果进行比较,证实了理论解的有效性和准确性。数值结果讨论了不同序列展开的影响,并强调了高阶展开的必要性。同时,还讨论了三维有限元法的应用范围。希望这种新的分析方法能对压电器件的优化设计有所启发。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Equivalent single‐layer Mindlin theory of laminated piezoelectric plates and application
Based on the Mindlin first‐order shear deformation theory, this paper proposes an equivalent single layer (ESL) plate theory to analyze the electro‐mechanical coupling problem of laminated piezoelectric plates (LPPs). The main features of the proposed approach are: (i) It assumes that the electric potential across the thickness is a polynomial function, ensuring its continuity at the interface. (ii) The electric displacements are continuous at the interface, in line with the interface continuity condition between laminated plates. The theoretical solutions for the deformation and electric potential of LPPs are obtained. The validity and accuracy of the theoretical solutions are confirmed through comparison with results of two‐ and four‐layer LPPs obtained from the three‐dimensional finite element method (FEM). The numerical results discuss the influence of different series expansions and emphasize the necessity of high‐order expansion. Meanwhile, the range of application of three‐dimensional FEM is discussed. It is expected that such a new analytical method can be instructive to the optimal design of piezoelectric device.
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