弱粘弹性材料结构振动特性分析的摄动解法

本文提出了“弱粘弹性”概念,用以描述弱时变材料的动态性能,并构造了弱粘弹性模型进行结构振动分析。根据“弱”的特点,选择了小参数,给出弱粘弹性材料动态性能的描述形式。在此基础上,构造了两种摄动解法,第一种基于弹性解,第二种基于单粘弹性模量解。文中还特别讨论了松驰函数为指数形式时的情形。

PERTURBATION METHODS FOR VIBRATION CHARACTERISTICS OF WEAKLY-VISCOELASTIC MATERIAL STRUCTURES

In the paper, the term "weakly-viscoelasticity"is presented to describe dyna mic behaviors of some weakly-time-varying materials, and a "weakly-visco elastic" model is constructed for the analysis of the structure vibration. Accor ding to the "weakly" features, a small parameter can be selected to derive the expression of the dynamic behaviors of the materials. And two perturbation methods are given. One is based on the elastic solutions, and the other is based on the single-viscoelastic-modulus solution. Especially the situation is discussed when relaxation functions are exponential.