EI、Scopus 收录
中文核心期刊

基于积分本构黏弹性带的横向非线性动力学

Transverse nonlinear nonplanar dynamics of an axially moving viscoelastic belt with integral constitutive law

  • 摘要: 研究了黏弹性传动带在1:1内共振时的横向非平面非线性动力学特性. 首先,利用Hamilton原理建立了黏弹性传动带横向非平面非线性动力学方程. 然后综合应用多尺度法和Galerkin离散法对偏微分形式的动力学方程进行摄动分析,得到了四维平均方程. 对平均方程的稳定性进行了分析,从理论上讨论了动力系统解的稳定性变化情况. 最后数值模拟结果表明黏弹性传动带系统存在混沌运动、概周期运动和周期运动.

     

    Abstract: In this paper, the problem of the transverse nonlinearnonplanar oscillations of an axially moving viscoelastic belt with theintegral constitutive law are investigated in the case of 1:1 internalresonance. The governing equations of this problem are firstly derived withthe generalized Hamilton's principle to obtain the in-plane and out-of-planetransverse nonlinear oscillations of the axially moving viscoelastic beltneglecting the axially deformation. Perturbation analyses are carried out onthese partial differential governing equations with the multiscale methodand the Galerkin's approach to obtain four-dimensional averaged equationsand to analyze the stabilities of the solution in the dynamic system. Thesimulation results show the periodic motion, the quasi-periodic motion andthe chaotic motion in the transverse nonlinear nonplanar oscillations of theaxially moving viscoelastic belt.

     

/

返回文章
返回