双材料自由阻尼层结构拓扑优化设计方法

Topology Optimization Design of Bi-Material Free-Layer Damping Treatments

目的在不减小板壳结构动刚度的前提下有效提高板壳结构的抗振性能,提出一种板壳阻尼复合结构拓扑优化设计。方法以结构模态阻尼比为目标函数,以某阶固有频率不小于设定值为约束条件,推导目标函数和约束条件对设计变量的灵敏度表达式,采用SIMP插值函数和移动渐近线法求解优化数学模型。结果研究表明,文中提出的双材料阻尼层结构相比传统单材料阻尼层结构的振动响应明显减小,同时适当改变设计目标和约束条件,可满足不同的工程应用需要。结论通过在宏观上对高刚度低阻尼材料和低刚度高阻尼材料的分布进行了设计,优化后的结构兼顾低刚度高阻尼材料的高阻尼特性和高刚度低阻尼材料的高刚度特性,实现了结构高刚度高阻尼的设计。

For the purpose of reducing vibration of plate/shell structures with given dynamic stiffness,this paper put forward a bi-material topology optimization method for damping material layout on plates/shell under the premise of structure dynamic stiffness.The modal loss factor of the structure was taken as the design objective,natural vibration frequency was taken as constraints for the optimal design of bi-material damping layer,sensitivity expression of the objective function and constraint conditions were deduced,the mathematical model was solved by SIMP(Solid Isotropic Material with Penalization)and MMA(Method of Moving Asymptotes)methods.Studies showed that the al bi-material layer damping structure can effectively reducing the structural vibration level and noise compared with the single material layer damping structure,it could meet different engineering application requirements by changing the design objective and constraints.The optimal bi-material layer damping structure obtained by designing the layout of the two damping material,which one is high stiffness and low damping material,the other is low stiffness and high damping material.