Concurrent optimization of actuator/sensor layout and control parameter on piezoelectric curved shells with active vibration control for minimizing transient noise

Although frequency-domain optimization approaches are commonly used for noise control, ubiquitous transient behaviors indicate that time-domain approaches cannot be ignored. Thus, this paper minimizes the transient noise radiated from the vibration system with constant gain velocity feedback (GGVF) control by combining topology optimization and parameter optimization. Based on the solid isotropic material with penalization (SIMP) model, the pseudo density is introduced to characterize the presence or absence of piezoelectric material. To satisfy engineering requirements, constraints on the usage amount of piezoelectric material, consumable energy, and maximum transient voltage are considered. Transient sound radiation is predicted by using a finite element/time-domain boundary element method (FEM/TDBEM). Sensitivity formulae of objective function to pseudo density and feedback gain are derived using a combination scheme. Namely, a direct method is applied to obtain the vibration sensitivity information at all boundary nodes, the results of which are input into the sensitivity calculation of transient sound radiation addressed by an adjoint variable method. This scheme integrates the advantages of the direct method which can calculate the vibration sensitivity of all nodes at once and of the adjoint variable method which has high computational efficiency. The gradient-based method of moving asymptotes (MMA) is employed to solve for optimised solutions. Numerical examples demonstrate the accuracy of the sensitivity formulae and the effectiveness of the concurrent optimization strategy.