Distributed piezoelectric actuator layout-design for active vibration control of thin-walled smart structures

This paper proposes a scheme for distributed piezoelectric actuator layout-design to improve active vibration control performance of thin-walled smart structures. The aim of the design is to maximize the energy transformation from actuator to structure so that better control performance will be achieved under a control strategy. The system performance index (SPI) is used to measure energy transformation. The layout-design problem is formulated by combining the topology optimization technique and the SPI. The pseudo-densities of piezoelectric materials are used as design variables and a penalty function is applied on piezoelectric materials so that a clear result can be obtained. Based on the chain rule and the adjoint method, and with the help of solving Lyapunov function, the sensitivity analysis is conducted. The optimization model is solved by nonlinear programming method. Once the optimized layout is obtained, the linear quadratic regulator (LQR) control strategy is applied and vibration suppression can be achieved. The method is load-independent. External loads and control strategy are not considered in layout-design so that a single layout can be obtained. Yet for all that, the optimized layout can achieve excellent performance in a wide range of load cases. Two numerical examples and two engineering applications demonstrate the validity of the proposed method.