考虑黏弹性材料随机性的被动约束层阻尼梁动力学分析

Dynamic Analysis of Passive Constrained Layer Damping Beam with Randomness of Viscoelastic Material

采用传递函数方法研究了阻尼层黏弹性材料随机性对被动约束层阻尼(PCLD)梁动力学特性的影响。由Hamilton原理建立了PCLD梁六阶运动微分方程,通过引入状态向量,建立了系统的状态空间方程,利用传递函数方法得到了梁的固有频率和损耗因子。以黏弹性材料分数导数模型中的参数作为基本的随机变量,并假设其服从正态分布,使用Monte Carlo直接抽样法考察了材料模型参数的随机性对结构固有频率和模态损耗因子的影响。计算结果表明黏弹性材料参数的随机性对梁动力学特性的变异系数影响较大,模态损耗因子的变异系数最大值是材料参数变异系数的4.5倍。

A dynamic analysis of the passive constrained layer damping（PCLD） beam considering randomness of viscoelastic damping layer was studied by using the transfer function method.With an introduction of the state vector,the governing equation of the PCLD beam in state space was established from the six-order differential motion equation,which was derived by using the Hamilton principle.The closed-form solutions of natural frequencies and loss factors of a PCLD beam were obtained by the distributed parameter transfer function method.The parameters in fractional derivative model of viscoelastic material were regarded as the base random variables,which follow normal distribution in this analysis.The influence of parameter randomness on the natural frequency and the mode loss factor of the structure were analyzed by using the Monte Carlo method.Numerical examples show that the randomness has obvious effects on the correlation coefficient of dynamic characteristic,and the maximal value of the loss factor＇s correlati on coefficient is about 4.5 times as much as the one of material parameter.So it is necessary to carry out the random analysis for PCLD structures.