主动约束阻尼板压电层电压拓扑优化研究

建立主动约束层阻尼板有限元模型，以结构模态阻尼比最大化为目标函数，压电层总电能消耗为约束条件，压电层单元控制电压为设计变量，对主动约束层阻尼板压电层电压进行了拓扑优化，获得了压电层电压最优拓扑分布。通过引入虚拟设计变量，将压电层电压控制不连续问题转化为连续问题。考虑实际工程应用的需要，采用指数函数对电压中间变量进行惩罚。在灵敏度分析基础上，采用移动渐进线(MMA)法，求解了主动约束层阻尼板电压拓扑优化问题。数值算例证实了电压拓扑优化模型以及数值求解方法的有效性。

TOPOLOGY OPTIMIZATION DESIGN OF ACTUATION VOLTAGE IN PLATES WITH ACTIVE CONSTRAINED LAYER DAMPING TREATMENTS

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.