The thermo-electro-mechanical vibration characteristics of piezoelectric nanoplates using Kirchhoff and Mindlin plate theories under a two-parameter elastic foundation with general boundary conditions are investigated in this article. Utilizing nonlocal elastic theory, the governing equations of the analytical model, which account for external variable influences, are derived using Hamilton’s principle. In the benchmark case, a wave-based method is employed to analyze the vibration characteristics of the piezoelectric nanoplate with general boundary conditions. Additionally, a series of detailed numerical examples are provided to examine the impact of the nonlocal parameter, external electric voltage, temperature change, biaxial force, Winkler’s modulus parameter, and Pasternak’s modulus parameter on the vibration characteristics of the piezoelectric nanoplate restrained on a two-parameter elastic foundation with general boundary conditions. The accuracy of the calculations is verified, and several conclusions are drawn. This paper aims to expand the numerical analytical range of vibration analysis for nanoplate structures and provide theoretical data for the design of nano-electromechanical systems.

中文翻译：

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一般边界条件二参数弹性基础下压电板的热机电振动分析


本文利用 Kirchhoff 和 Mindlin 板理论研究了具有一般边界条件的二参数弹性基础下压电纳米板的热机电振动特性。利用非局部弹性理论，利用哈密顿原理导出了考虑外部变量影响的分析模型的控制方程。在基准案例中，采用基于波的方法来分析具有一般边界条件的压电纳米板的振动特性。此外，还提供了一系列详细的数值算例来检验非局部参数、外部电压、温度变化、双轴力、温克勒模量参数和帕斯捷尔纳克模量参数对约束在双轴上的压电纳米板振动特性的影响。具有一般边界条件的参数弹性地基。验证了计算的准确性，并得出了几个结论。本文旨在扩大纳米板结构振动分析的数值分析范围，为纳米机电系统的设计提供理论数据。