一种稳健的移动绳振动计算的行波反射叠加法

A robust method of travelling wave reflection superposition for solving transverse vibration of axially moving string system

在工程设备中广泛应用的绳移系统以其振动问题而备受关注。针对传统有限元法及Galerkin方法对于高速移动绳横向振动计算误差大、易发散的问题,基于行波在不同边界的反射叠加技术,文章提出了一种有限长度轴向移动绳横向振动计算方法。结合其初始条件以及边界条件获得反射波的表达式,从而将移动绳横向振动等效为不同速度移动波及其反射波的叠加,推导出其理论表达式。以两端固定的定长轴向移动绳为算例,通过与基于有限元的Newmark-beta法及时变状态方程法比较,验证了反射叠加法具有更高的精度,对于高速移动工况具有更好的稳定性。

Axially moving string system which is widely used in engineering equipment has attracted much attention for its vibration problems.In view of the calculation error and the divergence problem of transverse vibration of the high-speed moving string in the traditional finite element method and Galerkin method,a calculation method for the transverse vibration of axially moving string system with finite length is presented based on traveling wave reflection superposition technology in different boundary conditions.Based on the initial and boundary conditions,the expression of reflected wave can be obtained.Transverse vibration is equivalent to the superposition of the travelling wave with different speed and the reflected wave,and its theoretical formula is derived.Compared with the Newmark-beta method and time-varying state space function method based on finite element discretization,the numerical example of axially moving string with both fixed ends and constant length shows that travelling wave reflection superposition method has higher precision and better stability in high-speed moving condition.