Abstract: The constrained layer damping plate with the damping layer having periodically distributed square holes was designed. The equivalent elastic tensors of the porous damping layer were calculated by using homogenization method. The finite element model of the constrained layer damping plate considering the homogenization of the porous damping layer was developed and its loss factor was calculated. The size of square cells was optimized to maximize the loss factor of the porous damping composite plate through searching the optimal equivalent shear modulus of the porous damping layer. The numerical example was given to demonstrate the effectiveness of the proposed approach. The results show that the optimization of the square cells can enhance vibration energy dissipation of the porous composite plate and achieve an effective attenuation of amplitudes. In addition, the consumption of the damping material can be reduced significantly. This method demonstrates a potential application in structural vibration control.

Key words: vibration and wave , constrained layer damping , homogenization , finite element method , loss factor , optimization

摘要： 将约束层阻尼板中的阻尼层设计成具有周期方孔胞元的多孔阻尼结构，采用均匀化理论，计算多孔阻尼层的等效弹性张量。建立均匀化的约束层阻尼板有限元模型，计算多孔阻尼复合板的损耗因子。以多孔阻尼层等效剪切模量为设计变量，以结构模态损耗因子最大化为目标函数，对多孔阻尼复合板中的阻尼胞元进行尺寸优化。给出数值算例，并与商业有限元软件计算结果进行对比，结果表明：采用均匀化理论，对多孔阻尼复合板中的阻尼胞元尺寸进行优化是可行的，采用优化后等效剪切模量设计的阻尼胞元尺寸，不仅阻尼材料用量大为减少，减振效果也有所增强，该方法对约束阻尼结构的优化设计具有一定指导意义。

关键词: 振动与波, 约束层阻尼, 均匀化, 有限元法, 损耗因子, 优化