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This study investigates nonlinear free and forced vibration analysis of bidirectional functionally graded porous (BDFGP) PZT-4/PZT-5H plates subjected to combined thermoelectric and electromechanical loading, focusing on the effect of bidirectional material gradation and porosity on the nonlinear dynamic response of piezoelectric structures. The finite element formulation is developed using the energy principle with sigmoid-type bidirectional distributions, i.e., axial and transverse direction, considering even and uneven porosity distributions. The governing equations were discretized using a nine-noded Lagrange element, with each node possessing seven degrees of freedom (DOFs), to accurately capture electromechanical coupling and geometric nonlinearity. Nonlinear free vibration is solved using an iterative method, while forced vibration is analyzed via Newmark time integration. This model is validated against available benchmark results to ensure its accuracy and reliability. Extensive parametric analyses were performed to evaluate the effects of bidirectional material gradation, porosity distribution, boundary conditions, and combined thermo-electro-mechanical loadings on the nonlinear dynamic responses. The analysis demonstrates pronounced variations in natural frequencies, displacement amplitudes, and stability margins as reflected in time-displacement, phase portraits, and FFTs. Overall, the study highlights the effectiveness of BDFGP structures in smart structural applications, offering promising potential for adaptive control and enhanced performance under complex thermo-electro-mechanical loading conditions.
Zhao et al. (Mon,) studied this question.