Topology optimization of piezoelectric curved shell structures with active control for reducing random vibration

Abstract

This paper investigates topology optimization of the surface electrode coverage on piezoelectric sensor/actuator layers attached to a curved shell structure subjected to stationary random force excitation, with the aim to minimize the random vibration response under active control. In the optimization model, the power spectral density (PSD) of displacement response at the specified point is considered as the objective function. The pseudo-densities describing the surface electrode distribution are assigned as the design variables, and an artificial active damping model with penalization is employed to suppress intermediate density values. The voltage across each actuator is determined by velocity feedback control law. Pseudo excitation method (PEM) is introduced to analyze random vibration response of a piezoelectric curved shell structure with active control. In this context, the adjoint variable method for the sensitivity analysis of displacement PSD with respect to topological design variables is derived. Numerical examples fully demonstrate the validity of the proposed approach.