小曲率粘弹性索非线性随机稳定性分析

基于Kelvin粘弹性材料本构模型,研究小曲率粘弹性索在窄带随机激励作用下的非线性随机稳定性及均方响应。首先建立小曲率粘弹性索数学模型;然后提出一种确定粘弹性索均方响应及概率渐近稳定性方法;给出了系统均方稳定对激励带宽、幅值、中心频率等要求;给出系统的稳定区域;最后讨论了材料粘性、波速比及介质阻尼对系统不稳定区域的影响。

Nonlinear Random Stability of Viscoelastic Cable With Small Curvature

The non-linear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied.The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material.Amathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first.And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted.Finally,the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.