Active control and prediction model for the dynamic shape of laminated plate/shell structures with piezoelectric actuators

This study establishes an active control and prediction model for the dynamic shape of laminated plates/shells with piezoelectric actuators. Firstly, transient responses of shell structures are numerically calculated by adopting the finite element method (FEM) and the Newmark formulae, then the Kuhn-Tucker equation is utilized to get the time-varying voltage values with a minimum shape control error. Subsequently, a backpropagation neural network (BPNN) is constructed to predict the control precision for cases with different piezoelectric actuator layouts. Finally, the proposed control model is demonstrated through numerical examples with a maximum relative control error of only 0.023% for a given desired shape and the average error of the prediction model with 98 input neurons is 18%, thereby satisfying the application requirements. Furthermore, for a model with 3870 degrees of freedom and 21 discrete time points, the computational time is reduced significantly from 8.24 s to 0.002 s through the prediction model, making it highly suitable for optimization problems by utilizing heuristic algorithms.