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本文研究了粘弹性阻尼结构动力特性的分析方法。根据分数导数模型表示的粘弹性材料本构方程,对一种阻尼材料用拟合法构造了它的力学性能解析表达式。建立了一种八自由度夹层梁有限元模型,从而给出了粘弹性阻尼结构的有限元动力学方程。为分析粘弹性阻尼结构的动力特性,提出了一种非线性特征值问题的迭代解法。应用上述方法对悬臂约束阻尼层梁的复模态参数进行了分析,并进行了实验验证。结果表明,分析与实验的结果一致,说明本文所提出的方法是可靠的且有较好的精度和实用性。
In this paper, the analytical method of dynamic characteristics of viscoelastic damping structures is studied. According to the constitutive equation of viscoelastic material represented by fractional derivative model, an analytic expression of mechanical properties of a damping material is constructed by fitting method. A finite element model of 8 DOF sandwich beam was established, and the finite element dynamic equation of the viscoelastic damping structure was given. To analyze the dynamic characteristics of a viscoelastic damping structure, an iterative method for nonlinear eigenvalue problems is proposed. The complex modal parameters of cantilever beam with damping layer were analyzed and verified by the above method. The results show that the analysis and experimental results are consistent, indicating that the proposed method is reliable and has good accuracy and practicality.