中文摘要：

为实现阻尼结构减振优化,从阻尼材料的力学本构出发,基于虚功原理建立了约束阻尼板动力学平衡方程,从阻尼耗能角度推导出模态损耗因子解析计算式。构建了以模态损耗因子最大且模态频率变动最小为目标、以阻尼材料用量为约束的阻尼板多目标优化数学模型。在对模态损耗因子及模态频率灵敏度进行推导的基础上,构建了归一化复合灵敏度算式,并引入拓扑渐进法求解优化模型。编制出阻尼板渐近法优化程序,并对阻尼板进行了优化仿真。结果显示,采用多目标拓扑渐进优化,既能大幅提高阻尼材料的减振效能,又能保证阻尼板频率特性的稳定,且可较大幅度地降低阻尼材料用量。对阻尼板进行了谐响应分析,验证了优化结果的有效性。该优化法在对结构动力学特性有严格要求的减振设计中存在应用前景。

英文摘要：

Aimed to realize vibration reduction of damping structure,constrained damping plate vibration optimization was studied.From the constitutive relations of damping materials,the dynamics equation of constrained damping plate was deduced by principle of virtual work,modal loss factor mathematical calculation formula was deduced based on the energy dissipation.A modal was built,which took maximum the modal loss factor and minimum modal frequency changes as the objective function,damping materials consumption as constraint conditions,the modal loss factor and frequency sensitivity formula was deduced,normalized composite sensitivity formula was constructed.Evolutionary structural optimization was introduced to solve the topological optimization mathematical model,A program of damping structure topological optimization process was given in order to realize simulation calculation of damping plates.The simulations show that multi-objective of the evolutionary structural optimization may significantly improve the vibration reduction effectiveness of the damping material,guarantee the stability of frequency characteristics of the damping plates and greatly reduce the dosage of damping materials.The harmonic response analysis was carried out on the damping plates to verify the effectiveness of the optimization results.The optimization method may be widely used in the design of vibration reduction which have strict requirements in structure dynamics characteristics.