The Dynamics Of Axially Moving Viscoelastic Beam With Time-variant Tension

The axially moving structure,as mechanical model of many engineering mechanism,can be found widely in actual production.It includes power transmission belt,elevator cable lifts,saw blades,textile fibers,conveyor belts,tapes,audio tapes,etc.One uniform characteristic of these structures is they all move along one certain direction.And the system will generate moderate acute transverse vibration.In the course of motion,the system will have a great lateral vibration.The application of the changeable axial velocity and variable tension plays a great role in the analysis of axial dynamics.The consideration of varied velocity and time-variant tension and the relationship between tension and velocity means much for the analysis of dynamics of axially moving structures,and these can be the base of some related research of further complex model.This dissertation focused on axially moving beam,and established the models of axially moving Timoshenko beam and axially moving Euler-Bernoulli beam respectively.The theoretical analysis and numerical validation are applied to research vibration characteristics of these two models.The synopses are list as following:1.The complex frequencies and complex mode of axially moving Timoshenko beam are invested.Firstly,the linear differential motion equations and related boundary conditions are given.Then,through complex modal method,we calculated the complex frequencies and the complex mode,and we investigated the influence of some different coefficients on the complex frequencies and the complex mode.At last,the differential quadrature schemes are used to verify analytical solution2.The linear vibration of axially moving beam with time-variant tension is researched.Firstly,the relationship of periodic varying tension and velocity are calculated and the motion equations and related boundary conditions of this model are founded.Secondly,through the method of multi-scales,solving conditions is obtained and then mode function and natural frequency are derived;at the same time,the effects of with or without 1:3 internal resonances on stability are taken into account.Thirdly,the differential quadrature scheme is used to verify analytical solution.3.The nonlinear vibration of axially moving beam with time-variant tension is researched.Firstly,during the process of founding moving equations and boundary conditions of linear model nonlinear term is added in.then,Multi-scale method isadopted to analyze steady state response of the system.Finally,some specific numerical instances are listed to describe the influence of different coefficients on the steady response of the system.