Nonlinear dynamic response and stability of piezoelectric shells with piezoelectric nonlinearities

• Nonlinear FEM for PLS with MITC elements, addressing both geometric and piezoelectric nonlinearities. • Piezoelectric nonlinearity alters structural stability, depending on voltage polarity. • Higher-order harmonic effects arise under harmonic excitation due to piezoelectric nonlinearity. • Enhanced active vibration control with reduced RMS voltage overestimation compared to linear models. Most existing research on mechanical analysis of piezoelectric laminated shells focuses primarily on linear piezoelectric constitutive equations and small rotations under the von Kármán assumption. However, these studies rarely address the inherent nonlinear effects of piezoelectric materials and the significant geometric nonlinearities due to large displacements and rotations that frequently occur in practical engineering applications. To address this gap, this paper first applies the mixed interpolation of tensorial components (MITC) technique to a numerical model of piezoelectric laminated shells that simultaneously considers both geometric and piezoelectric nonlinearities. A comprehensive nonlinear analysis method is established to analyze post-buckling behavior, nonlinear dynamic response, and dynamic control of piezoelectric laminated shell (PLS) structures. Based on the Reissner-Mindlin shell theory, the MITC elements effectively solve the shear-locking issue in numerical analysis. Using piezoelectric nonlinear constitutive relations and the covariant Green-Lagrange strain field to describe large displacements and rotations of PLS, the full nonlinear control equations of the structure are derived through Hamilton's principle and the total incremental formulation. The post-buckling analysis uses the generalized displacement control method, while the dynamic response is solved using the Newmark-β method. By comparing with existing literature, the accuracy of the proposed model in capturing piezoelectric nonlinearity and geometric nonlinearity effects is verified. Additionally, the impact of piezoelectric nonlinear parameters on the post-buckling responses, nonlinear dynamic response, and active control effects of PLS is studied in detail. It is found that piezoelectric nonlinearity affects the structural instability characteristics, leads to richer nonlinear phenomena, and provides better active control performance. This study offers theoretical guidance for the stability design and control technology of structures in engineering practice.