Nonlinear dynamic response of functionally graded plates with piezoelectric nonlinearity

作者：Yu Zhang, Hongyun Zhu, Shaoyu Zhao, Zhi Ni, Chaofeng Lü, Jie Yang · 发表于：European Journal of Mechanics - A/Solids · 年份：2025 · DOI：10.1016/j.euromechsol.2025.105776 · 被引用次数：21 · 研究领域：Composite Structure Analysis and Optimization、Structural Analysis and Optimization、Aeroelasticity and Vibration Control

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 e...