基于优化准则法的自由阻尼材料拓扑优化

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Based on SIMP,a topologic optimization model for a free damping material was established with the maximum modal damping ratio as a goal,damping material volume as a restriction and densities of damping material cell as design variables.The sensitivity of modal damping ratio to densities of damping material cell,and the updating criterion of design vaviables were derived.Then,the topologic optimization program for a free damping meterial based on the optimization criteria method was developed using the direct matrix abstraction program（DMAP） of MSC.Nastran.The structure-acoustic coupling model of an aluminum plate and an acoustic cavity was taken as an example.With this program and the FE method,the arrangement of damping material on the aluminum plate was optimized to maximize the damping ratio of the first order bending mode of the system,the result was verified with tests.The two damping treatments of fully damped one and partly damped one after optimized were compared with no damping material treatment.It was shown that after treated,the acoustic pressure at the reference point drops 110.6Pa and 107.7Pa,respectively in simulations,while it drops 22.47Pa and 20.91Pa,respectively in tests;the comparison verifies the effectiveness of the topologic optimization program.基于各向正交惩罚材料密度法,建立了以自由阻尼结构模态阻尼比最大化为目标,以阻尼材料体积为约束条件,以阻尼材料单元相对密度为设计变量的拓扑优化数学模型。推导了模态阻尼比对阻尼单元相对密度的灵敏度和设计变量的更新准则,基于优化准则算法用MSC.Nastran的DirectMatrixAbstractionProgram语言编制了通用的阻尼材料拓扑优化程序。以一铝板-声腔耦合系统为对象,以结构一阶弯曲模态阻尼比最大为目标,利用该拓扑优化程序和有限元分析方法对铝板上的阻尼材料进行优化布置,并用试验进行了验证。把铝板全阻尼处理和拓扑优化后部分阻尼处理的降噪效果进行对比,在仿真环境中,参考点处声压分别下降了110.6Pa和107.7Pa,在实验条件下,参考点处声压分别下降了22.47Pa和20.91Pa,从而验证了优化方法的有效性。