等速输送运动纱线的横向振动分析

本文讨论在非齐次边界条件下由端点运动激励的纱线强迫振动问题。首先讨论了相应的齐次方程的特征值问题,给出了两端无横动时等速移动(即等速输送运动)纱线的各阶固有频率与复振型函数。然后,利用傅立叶级数理论寻求非齐次边界条件下的齐次方程的解,从而求出了等速输送纱线在卷绕端运动激励下的稳态响应的精确解。

TRANSVERSE VIBRATION OF A THREADLINE TRAVELLING AT CONSTANT-SPEED

In this paper, the author discusses the forecd transverse vibration problem of the constant-speed travelling threadline, excited by a guido-eyelet traverse motion, under inhomogeneous boundary conditions. First, the eigonvalue problem of the corresponding homogeneous equation is investigatod to obtain all the natural frequencies and complex modal functions of the travelling thareadline passing through two fixed guide-eyelet. Secondly, the author uses Fourier series expansion to find the solution of the above-mentioned equation under inhomogeneous boundary conditions, thus obtaining the steady response of the constant-speed travelling threadline to the motion excited by the thread-guide traversing at the wound package end.