Topology optimization of piezoelectric layers in plates with active vibration control

Abstract

This article investigates topology optimization of the piezoelectric actuator and sensor layers in a plate for achieving the best vibration control performance. Therein, the actuator patches and sensor patches are symmetrically attached to the host layer, and the classical negative velocity feedback control strategy is adopted for reducing the vibration level of the structure. In the optimization model, the dynamic compliance under a specific excitation frequency or the aggregated dynamic compliance in a given frequency range is taken as the objective function. The relative densities of the elements in the actuator layer and the sensor layer are considered as topological design variables. The optimization problem is then formulated by using an artificial material model with penalization for both mechanical and piezoelectric properties. It is pointed out that the global-level damping property, consisting of the structural damping and the active damping effects, is a nonproportional one. For alleviating the computational burden involved in the frequency response analysis, the dynamic equations are solved with the complex mode superposition in the state space after a model reduction transformation. In this context, the sensitivity analysis scheme is also derived. The effectiveness and efficiency of the proposed method are demonstrated by numerical examples.