Integrated design optimization of structure and vibration control with piezoelectric curved shell actuators

The investigation focuses on simultaneously optimizing the locations and thicknesses of piezoelectric curved actuators as well as transient control voltages to achieve the best performance index. A curved shell element is deduced and the nodal displacement constraint equations are used to couple the piezoelectric curved shell element and the base shell element. Then the dynamic finite element equations of the piezoelectric shell structure are formulated. Based on the optimal vibration control theory, an integrated design optimization model is proposed. The linear quadratic performance index is taken as the objective function, and the control voltages as well as the number and volume of the actuators are considered as the constraints. The design variables include not only the locations and control voltages but also the thicknesses of the piezoelectric actuators. A two-layer optimization scheme is proposed to address this optimization problem with discrete and continuous variables coexisting. Because the control voltage is transient and time-varying, the linear quadratic optimal controller is used for the optimal control voltages in the inner layer. A simulated annealing algorithm is employed to optimize the locations and thicknesses of actuators in the outside layer. Numerical examples are implemented to demonstrate the accuracy of the curved shell element, the validity of the theoretical model, and the feasibility and effectiveness of the proposed optimization scheme.