Dynamic topology optimization of piezoelectric structures with active control for reducing transient response

• Topology optimization of active structure is treated to minimize transient response.
• We introduce CGVF control into topology optimization for piezoelectric structures.
• Layout design method of the actuator/sensor layers under dynamic excitations is proposed.
• Adjoint-variable sensitivity analysis for a general integral function is derived.
• The method can be employed to optimize vibration control performance under impacts.

This paper investigates topology optimization of the piezoelectric actuator/sensor coverage attached to a thin-shell structure to improve the active control performance for reducing the dynamic response under transient excitations. The constant gain velocity feedback (CGVF) control algorithm is considered and the structural dynamic response under the corresponding active damping effect is evaluated with a direct time integration method. In the mathematical formulation of the considered topology optimization model, the time integral of the displacement response over a specified time interval of interest is taken as the objective function. The pseudo-densities describing the piezoelectric material distribution are taken as the design variables, and a penalization model on the structural stiffness and piezoelectric effect is employed. The adjoint-variable sensitivity analysis scheme for a general integral function within a given time interval is derived, which facilitates a gradient-based mathematical programming solution of the optimization problem. Numerical examples demonstrate that the proposed method can generate meaningful optimal topologies of piezoelectric layers. Also, the influences of the control gain and the integration time intervals in the objective function on the optimal solutions are discussed. The proposed method can be used for providing useful guidance to the layout design of the actuator/sensor layers attached to a thin-shell structure subject to dynamic excitations, in particular impact forces. It is also confirmed that the achieved vibration reduction is mainly due to improvement of the active control performance rather than changes of the structural dynamic stiffness/mass property.