Research On Calculation Vibration Energy And Nonlinear Experimental For An Axially Travelling String System

The axial travelling string system is one of the important forms of mechanical transmission,which has the advantages of high efficiency and flexible layout.However,the string bending stiffness is small and showing flexible structural features,the system is easily produced the transverse vibration that seriously affecting the stability and accuracy under external excitation,which limited the application of axially travelling string system.In order to perform the vibration effective control,the transverse vibration of the axially travelling string should be has an intensive discussed.In this thesis,the calculation and analysis of the transverse vibration energy and the nonlinear dynamics of axially travelling string system is researched.In this thesis,the axial travelling string system is taken as the research object.Firstly,the simplified model of axially travelling string system is established.Based on the finite element method,the length of the string on the space is divided into a finite element with the same length,which the transverse vibration problem of moving string is transformed into finite element transverse vibration.Secondly,the transverse vibration energy of string system obtained by appropriate simplification and substitution,it was proved that the transverse vibration energy of the fixed length string is periodically changed in theory proof and numerical simulation.Then,the nonlinear transverse vibration equation of the viscoelastic axially travelling string system with Kelvin model is established based on the engineering application,Galerkin method and modified Four-order Runge-Kutta method are proposed for solving the nonlinear dynamic equations.The nonlinear transverse vibration of the viscoelastic string and the nonlinear dynamic phenomena of the system are studied respectively.Finally,the experiments of axially travelling belt are presented.It was shown that there are many scenarios for periodic motion,chaotic motion and beat frequency phenomena to be present and measured in the vibration of the axially travelling belt which provided for the theoretical study of the nonlinear transverse vibration theory.