中文摘要：

研究阻尼结构的阻尼材料最优布局问题。基于虚功原理,构建约束阻尼板振动微分方程,从约束阻尼板若干基本假设出发并根据阻尼板自由振动微分方程,推导了结构模态阻尼比表达式。建立了以阻尼单元相对密度为拓扑设计变量,模态阻尼比最大为优化目标,阻尼材料用量为约束的阻尼结构拓扑优化数学模型。以阻尼单元模态阻尼比敏度为寻优方向的依据,采用增材式渐进法（AESO）求解优化模型,并依据拓扑优化准则在结构上不断敷设阻尼材料。编程实现了AESO算法,仿真计算表明：采用AESO优化时,阻尼材料主要敷设于结构的模态应变较大位置,且不会产生棋盘格现象,并且优化后的结构一阶模态阻尼比较优化前可增加83.6%,而常规渐进法带来的增幅仅72.13%。为进一步验证优化效果,还对结构进行了谐响应分析,结果表明采用增材式渐进法优化时,结构可获得更佳减振效果。

英文摘要：

In this paper, the structural damping material optimal layout is studied. Based on the principle of virtual work, the vibration differential equation of damping plate is built. According to related basic hypothesis of constrained damping structure, the structural modal damping ratio expression is deduced by free vibration differential equation. The model useing damping material unit relative density as design variables, the structural damping ratio maximization as topology optimization goal, damping materials dosage as topology optimization constraint condition is set up. In order to obtain accurate numerical solution, the model is solved by AESO algorithm, calculating the modal damping ratio acuity to provide the best search direction for optimization iteration. According to the topology optimization criterion, damping materials is added gradually. The AESO optimization is realized by program. A numerical example shows that based on AESO method for damping structure, damping materials are mainly placed on the maximum mode strain locations of the structure. The checkerboard phenomenon is avoided. After AESO for the structure, the first order damping ratio is increased by 83.6%, while after ESO for the structure, the number is 72.13%. To verify topology optimization result, harmonic response analysis is carried out on the damping structure; the result shows that by the AESO optimization, structure vibration suppression effect is better.