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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.

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Simultaneous optimization of multiple parameters of an active structural acoustic control system under random force excitation is presented in this article. A method integrating the pseudo excitation method, finite element method, and boundary element method is proposed to analyze the random acoustic radiation. The active structural acoustic control of randomly vibrating structures is developed using the velocity feedback control scheme with the help of the pseudo excitation method. The acoustic design optimization model is proposed, in which the auto power spectral density of sound pressure is taken as the objective function and the placements of actuators/sensors as well as control gains are assigned as design variables. Taking into account the operational efficiency and control cost, the number of actuators/sensors and the total actuation energy are considered as constraints. A simulated annealing algorithm is employed for the optimization problem with discrete and continuous variables coexisting. Numerical examples are given to demonstrate the effectiveness of the proposed methods and the programs, and several key factors on the optimized designs are also discussed.