轴向运动纱线非线性动力学

以两端约束的轴向运动纱线为分析对象，建立了相应的线性波动方程。采用Galerkin截断法，获得了描述轴向运动纱线的横向振动一阶近似常微分方程。基于多尺度法，重点研究了系统主参激共振时系统的稳定性问题，获得了稳定性临界曲线的近似解析表达形式。研究结果表明，稳定性区域与轴向运动平均速度V0及波动速度幅值V1密切相关，V0与V1越大，不稳定区间越宽。

Nonlinear Dynamics of an Axially Moving Yarn

The initial-boundary-value problems of a linear wave equation of an axially moving yarn are considered.The ordinary differential equation of the first order approximate motion is derived based on the Galerkin truncation to deseribe the transversal vibration of the yarn,and the principal parametric resonance of the system is then analyzed using the method of multiple scales.The equations of approximate transition curves in the plane of the dimensionless frequency and excitation parameter that separate stable from unstable solution are derived.Results show that the unstalbe region is closely related to the average velocity V_0 and the small speed amplitude of the harmonic motion V_1 of the yarn,that is,with the increase of both V_0 and V_1,the unstable region become wider.