黏弹性材料Biot模型参数确定及其在黏弹阻尼结构中的应用

Biot model parametric determination of viscoelastic material and its application in viscoelastic damping structure

黏弹性材料广泛用于工程结构减振降噪,其本构模型的研究对黏弹阻尼结构的动力学分析具有重要的意义。Biot模型能够真实反映黏弹性材料参数随着频率变化的动力学特性;提出了一种确定其参数并将其结合到黏弹阻尼结构有限元动力学方程的方法;通过对频域内试验测得的黏弹性材料储能模量和损耗因子数据进行多参数非线性曲线拟合,并将其转化为在复频域内带约束条件的非线性优化问题,可以使非线性多参数确定问题大大简化;借助辅助耗散坐标将黏弹性材料Biot模型引入到黏弹阻尼结构有限元动力学方程中并转化成常规的二阶线性微分方程,实现了求解的简化。通过试验研究对该方法进行了验证,结果表明提出的Biot模型参数确定和有限元相结合的方法是正确、简单和有效的。

Viscoelastic materials are widely used to reduce vibration and noise in engineering structures.Their constitutive model study is of great significance to dynamic analysis of viscoelastic damping structures.Biot model can actually reflect dynamic characteristics with variation of frequency of viscoelastic material’s parameters.Here,a method for determining its parameters and combining Biot model with the finite element(FE)dynamic equation of viscoelastic damping structure was proposed.Multi-parameter nonlinear curve fittings were performed for data of viscoelastic material energy-storing modulus and loss factor obtained in frequency domain tests,and these fittings were converted into a nonlinear optimization problem with constraints in complex frequency domain to greatly simplify a nonlinear multi-parameter determination problem.Biot model of viscoelastic material was introduced into the FE dynamic equation of a viscoelastic damping structure by means of auxiliary dissipative coordinates,and then the FE dynamic equation was converted into second-order linear ordinary differential equations to realize simplification of solving.Finally,the proposed method was verified with tests.Results showed that the proposed method is correct,simple and effective.