黏弹性轴向运动变张力梁非线性动力学

摘要

在黏弹性轴向运动梁横向参数振动的非线性动力学行为研究中，首次计入因速度变化引起的、沿梁的径向变化的、轴向变张力的影响。给出描述变张力轴向运动梁横向非线性振动的偏微分—积分控制方程。基于微分求积法给出轴向运动梁横向非线性参数振动的数值解，通过观察梁中点的位移、速度随时间变化的历程，识别轴向运动系统的非线性动力学行为。同时，通过从数值解中提取的相图、Poincaré映射图和频谱分析，考察轴向运动梁横向振动的分岔与混沌特性，揭示了工程应用中的非线性轴向运动系统的混沌动力学行为。%The nonlinear behavior of the transverse parameter vibration of axially moving viscoelastic beams was investigated. The effect of the varying tension due to varying speed was considered for the first time. The longitudinal varying tension was introduced to establish the integro-partial-differential governing equations to describe the transverse vibration of the beams. Based on the numerical solutions by the differential quadrature method, the nonlinear dynamical behaviors like chaos were identified by the observation of the courses of displacement and velocity changing with time at the midpoint of the beam. Meanwhile the phase plane, the Poincaré map and the spectral analysis method were used to indicate the bifurcation and chaotic motions occurring in the transverse vibration of the axially accelerating viscoelastic beam. This work reveals the chaotic behaviors of nonlinear axially moving systems in engineering applications.