Thermo-electro-mechanical vibration analysis for piezoelectric plates under two-parameter elastic foundation with general boundary conditions

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.