基于哈密顿原理轴向运动纱线的振动特性研究

Research on vibration characteristics of axial yarn movement based on Hamilton′s principle

为获得任意载荷作用下轴向行进纱线任意点的横向位移参数,建立了轴向运动纱线在哈密顿体系下无量纲动力学微分方程。通过应用最小变分原理得到运动纱线的对偶方程,用分离变量法计算轴向运动纱线系统的各阶特征值和特征函数;基于线性辛特征值得到非奇异模态函数,推导出了模态函数的辛共轭正交归一关系;根据特征值及其分岔规律,分析纱线横向运动的稳定性,并利用非奇异模态函数分析纱线自由振动和受迫振动的位移响应;依据纱线横向振动的近似解,分析运动纱线在不同运行状态下的动力学行为。结果表明,纱线运动速度对响应周期、不同质点的响应幅值以及构形有较大影响,前2项构形经叠加即可求得纱线位移。

In order to obtain the lateral displacement of an axially moving yarn at any point under arbitrary load,the dimensionless dynamic differential equation of the axially moving yarn in Hamilton system is established.The axial movement of the yarn system conjugate symplectic eigenvalue was solved using minimum yarn dual variational principle of motion equation together with the variable separation method.A nonsingular modal function was obtained using the linear characteristic eigenvalues,and a modal function of conjugate symplectic orthogonal to a relationship was deduced.According to the eigenvalues and the bifurcation,the stability of the lateral movement of yarns was studied.Based on the approximate solution of the nonlinear lateral vibration,the dynamic behavior of the yarn under various operating conditions were studied.The results show that the yarn speed have obvious effect on the response cycle,the response amplitude of the different points and the yarn configuration.The yarn displacement can be obtained by superposition of the first two configurations.