构建了以模态阻尼比为目标函数，阻尼材料用量为约束条件的拓扑优化模型。分析了模态阻尼比对基结构单元的灵敏度，导出了灵敏度表达式。在此基础上，提出了基于一种进化方式的约束阻尼材料优化配置方法。给出了几个典型算例，获得了满足阻尼材料用量的约束阻尼材料最优拓扑构型。研究表明：文中提出的优化模型和准则是正确的，能有效应用于约束阻尼材料的优化配置，为优化阻尼材料分布，降低结构振动与噪声，开辟了崭新的技术途径。

Abstract: An Optimality Criteria is proposed to achieve the optimal placement for constrained damping material in structures. The topology optimization model is presented in which modal damping ratio is designed as an objective function, while constrained damping material consumption is considered as a constraint. The sensitivity of modal damping ratio to damping cell element is analyzed and derived. Furthermore, the formula is used to delete or keep damping cell elements in structures. The numerical examples are demonstrated to verify the effectiveness of the proposed optimality criteria and topology optimization method. The optimal placement of constrained damping material in structures is obtained. The obtained results show the validity of the proposed topology optimization Therefore, a potential application is demonstrated in vibration and noise control of damping structures as a new technical approach.