Thermo-electro-mechanical vibration analysis of piezoelectric nanoplates resting on viscoelastic foundation with various boundary conditions

Abstract

Based on the nonlocal Kirchhoff plate theory, the thermo-electro-mechanical vibration responses are studied for a rectangular piezoelectric nanoplate resting on viscoelastic foundation with various boundary conditions. In doing this, the governing equations of motion are first derived for vibration analysis, where thermo-electro-mechanical loadings, nonlocal effect, piezoelectric effect and viscoelastic foundation have been taken into consideration. Subsequently, the Galerkin strip distributed transfer function method is proposed to solve the governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for piezoelectric nanoplates with arbitrary boundary conditions. Here, the developed mechanics model is first validated by comparing the obtained results with those available in the literature. Also, the effects of nonlocal parameter, boundary conditions, viscoelastic foundation, external electric voltage, increment temperature, biaxial force and geometric dimensions on the vibration behaviors are carefully examined for the piezoelectric nanoplate. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanoplates, viscoelastic foundation and thermo-electro-mechanical loadings.