约束阻尼板的黏弹性阻尼层细观拓扑优化设计

Mesoscopic Topology Optimization of Viscoelastic Damping Layer for Constrained Layer Damping Plate

针对约束阻尼板的减振优化设计问题,提出一种约束阻尼板的黏弹性阻尼层细观拓扑优化方法。黏弹性阻尼层由三维单胞组成,采用代表体元法对三维单胞的等效材料属性进行分析。在对三维单胞施加边界条件时,考虑三维单胞上下表面受到约束层和基层约束的影响,在此基础上建立约束阻尼结构的宏观有限元模型。以宏观结构模态损耗因子最大化为优化目标,建立约束阻尼结构的黏弹性阻尼层细观结构拓扑优化模型。分析了优化目标函数关于设计变量的灵敏度,采用优化准则法对建立的优化模型求解。对建立的周期开孔的约束阻尼板有限元模型进行模态分析,与细分网格法对比,考虑边界约束的代表体元法计算得到的固有频率和模态损耗因子最大误差分别为0.09%和3.60%,而传统均匀化方法计算得到的固有频率和模态损耗因子最大误差分别为1.18%和6.59%,可见考虑边界约束的代表体元法的计算精度要高于传统均匀化方法。以黏弹性阻尼材料体积分数0.4为约束条件,分别以一阶、二阶和三阶模态损耗因子最大化为优化目标,对约束阻尼板的黏弹性阻尼层细观构型进行优化。结果表明,黏弹性阻尼层细观优化构型与目标阶次的模态振型和模态剪切应力方向相关;在黏弹性阻尼材料使用量减少了60%的情况下,优化结构的目标一阶、二阶和三阶模态损耗因子分别增加了3.70%、14.86%和10.22%,共振响应峰值分别减小了9.71%、10%和13.33%,验证了优化方法的正确性和有效性。

A mesoscopic topology optimization for viscoelastic damping layer of constrained layer damping(CLD)plates was proposed to solve the problem of vibration reduction optimization of CLD structures.The viscoelastic damping layer consisted of 3D unit cells.Representative volume element(RVE)was used to analyze the equivalent material properties of 3D unit cells.The imposed boundary conditions on the 3D unit cells of the viscoelastic layer were considering rigid skin effects.A mesoscopic topology optimization model for viscoelastic damping layer of CLD structure was established to maximize the modal loss factor of macrostructure.The sensitivities of the objective function with respect to the design variables were analyzed and the design variables were updated by optimality criteria(OC)method.The modal analysis of finite element model of periodic perforated CLD plate was carried out.Campared with fined-mesh method,the maximum errors of natural frequency and modal loss factor calculated by RVE considering rigid skin effects were 0.09%and 3.60%,respectively.However,the maximum errors of natural frequency and modal loss factor calculated by the traditional homogenization method were 1.18%and 6.59%,respectively.It could be seen that the calculation accuracy of RVE considering rigid skin effects was higher than that of the traditional homogenization method.With the volume fraction of viscoelastic damping material being 0.4 as the constraint,the meso-configuration of viscoelastic damping material of CLD plate was optimized with the first,second and third order modal loss factor maximization as the optimization objective.The results showed that the meso-configuration of viscoelastic damping layer was related to the modal shape of the target order and the direction of modal shear stress.Although the consumption of viscoelastic damping material was reduced by 60%,the first three modal loss factors of the optimized structure increased by 3.70%,14.86%and 10.22%,respectively.The resonant peaks decreased by 9.71%,10%and 13.33%,respectively.The correctness and effectiveness of the proposed optimization method were verified.