Nonlinear dynamic response of functionally graded plates with piezoelectric nonlinearity
Yu Zhang, Hongyun Zhu, Shaoyu Zhao, Zhi Ni, Chaofeng Lü, Jie Yang
Abstract
Piezoelectric functionally graded plates (PFGPs) always undergo large deformations, strong electric fields, and high-temperature variations in practical applications. Accurate prediction of their nonlinear steady-state responses under coupled thermo-electro-mechanical conditions requires accounting for both piezoelectric nonlinearity and temperature dependence, particularly under high-temperature variations and strong electric fields. This study investigates the frequency-amplitude response characteristics of PFGPs under such conditions. Using von Kármán nonlinear strain-displacement and nonlinear piezoelectric constitutive equations incorporating temperature effects, a nonlinear finite element model is developed based on higher-order shear deformation theory and Hamilton’s principle. The frequency-amplitude response is computed using an efficient Galerkin averaging-incremental harmonic balance method (EGA-IHB) combined with arc-length continuation facilitated by tensor contraction and FFT techniques. Model accuracy is validated through comparisons with existing literature and COMSOL simulations. Based on the dual-nonlinearity model, we analyze piezoelectric nonlinear effects under various electrical and mechanical conditions. Furthermore, the coupling impact of piezoelectric nonlinearity and temperature-dependent properties on the frequency-amplitude response are revealed. The results show that these factors lead to issues, including multiple solutions, hardening nonlinear effects, and curvature shifts in the frequency-amplitude response, especially under large thermo-electro-mechanical loads. This study provides a theoretical foundation for modeling nonlinear steady-state vibrations of PFGPs considering material nonlinearity.