Abstract：A topology optimization approach is proposed to attenuate the vibration of plates with Active Constrained Layer Damping (ACLD) treatments through the optimal spatial distribution of the actuation voltage in piezoelectric actuator layer. A finite element model of laminates with two piezoelectric layers is established based on energy approach. The optimal distribution of the actuation voltage is formulated as a discrete optimization problem with two-level control voltage design variables, where structural modal damping ratio characterizing the vibration energy dissipation is to be maximized under a constraint on the control effort. Such a optimization problem is then transformed into a continuous one by introducing element-wise artificial design variables defining the topological feature of the actuation voltage distribution in piezoelectric constrained layer. A power-law function relating the design variables and the applied control voltages is proposed to penalize intermediate values of the design variables. The optimization problem is then solved effectively by using the Method of Moving Asymptote (MMA) algorithm tailored for the constrained voltage optimization problem based on the sensitivity analysis. Numerical examples demonstrate the validity of the proposed problem formulation and numerical approach.
2012, Vol. 33 
