固定-阻尼边界定长轴向移动绳振动的行波边界反射叠加法  

A superposition method for vibration of travelling string with constant length based on moving waves reflected at fixed-dashpot boundaries

作　　者：陈恩伟[1] 张凯[1] 王军 魏浩征[1] 陆益民[1] CHEN En-wei;ZHANG Kai;WANG Jun;WEI Hao-zheng;LU Yi-min(School of Mechanical Engineering,Hefei Univ ersity of Technology,Hefei 230009,China;Intelligent Manufacturing Instit ute,Hefei University of Technology,Hefei 230009,China)

机构地区：[1]合肥工业大学机械工程学院,安徽合肥230009 [2]合肥工业大学智能制造技术研究院,安徽合肥230009

出　　处：《振动工程学报》2018年第5期870-874,共5页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51675150;51305115)

摘　　要：可简化为轴向移动绳系统的各类工程设备,诸如绳系卫星缆绳、缆车索道、物料输送带等,因其横向振动问题而备受关注,当前针对轴向移动绳的研究,大多集中在典型边界条件的基础上,而对于非典型边界条件的研究十分缺乏。基于经典的行波反射理论,以非典型边界的轴向移动绳为例,研究一种行波边界反射叠加法,通过左右行波在移动绳两侧边界的反射,结合其初始条件以及两侧边界连续性条件获得反射波的表达式,进而分三个阶段推导反射过程,最终通过叠加得出移动绳横向振动的解析表达式。以一端固定,另一端带有阻尼的定长度轴向移动绳为算例,结合中心差分法,通过MATLAB仿真,验证了行波边界反射叠加法的正确性和优越性。The vibration problem in the various engineering equipment is widely concerned,such as the cable of the tethered satellite,aerial ropeway,material conveyer belt,which can be simplified as the axially moving string system.At present,the research on axially moving string system mostly concentrates on the classical boundary conditions while few on the non-classical boundary conditions.In this paper,a traveling wave boundary reflection superposition method is studied based on the classical theory of traveling wave reflection.Taking the axially moving string with non-classical boundary conditions for example,the expressions of the reflected waves are obtained through the reflection of the left and right traveling waves on both sides,with considering its initial conditions and the continuity conditions of both sides.Then the reflection processes are deduced in three phases and finally its determinate expressions of transverse vibration are obtained.Take the axially moving string with a fixed boundary as well as a dashpot boundary for example,the correctness and advantages of the method of boundary reflection superposition are verified by MATLAB simulation combined with central difference method.

关 键 词：轴向绳移系统 非典型边界 横向振动 边界反射 

分 类 号：TB123[理学—工程力学] O327[理学—力学]