Nonlinear multi-point impacts of the bi-stable functional gradient magneto-electro-elastic plate: Interaction analysis and active control strategy based on bistable configuration

Revealing the coupling correlations between stiffness nonlinearity and magneto-electro-mechanical effect in multi-point impacts contributes significantly to the advancement of intelligent morphing structures. Multi-point impact responses and active control of bi-stable functional gradient magneto-electro-elastic (FG-MEE) plates are investigated, focusing on influence mechanism of the active control performance and the bi-stable characteristics. Based on the Reddy high-order shear plate theory model, the nonlinear geometric relationship considering the bi-stable configuration is established, and the multi-point impact model is extended. To achieve efficient structural design in multi-point impacts, the active control strategy in multi-physics fields is introduced. In the multi-physical field, the nonlinear dynamic model for multi-point impact involving the bi-stable functionally graded magneto-electro-elastic plate is established. The expanded two-step perturbation method is proposed to solve the bi-stable configuration driven by the magneto-electro-mechanical effect. To obtain the approximate solution for the multi-point impact of the bi-stable FG-MEE plate, the extended two-step perturbation method-Galerkin method is further developed to the higher-order form. Ultimately, coupling correlations between stiffness nonlinearity and magneto-electro-mechanical effect in the multi-point impacts are systematically revealed, and the active control performance is evaluated under the influence of multi-point impact.