轴向移动绳固有频率计算和分析

Calculation and analysis of natural frequency for an axially moving string

文章以轴向移动绳为研究对象,分析了定长度和变长度2种移动绳系固有频率和受迫振动特性。利用传播波在绳中反射的振动周期和固有振型规律,研究了轴向移动绳振动特性;通过Matlab数值仿真,对比了定长度和变长度2种移动绳固有频率的差异以及绳系的轴向移动速度和张紧力变化对其固有频率的影响;并利用四阶Runge-Kutta法,计算了轴向移动绳受迫振动的横向位移响应。

Aiming at an axially moving string with constant and variable length, the problems of natu- ral frequency and forced vibration are investigated. Dynamic characteristics of axially moving string are studied by vibration period and natural mode of transverse wave on the string. The difference in natural frequency between axially moving string with constant length and that with variable length is obtained by numerical simulations using Matlab. The relationship between the natural frequency and the axial speed and tension is obtained. Transverse displacement response of forced vibration is ob- tained by numerical simulations using fourth-order Runge-Kutta method.