Boundary Damping Control Of Axially Travelling String System Based On Vibration And Energy Dissipation

Axially travelling string system represents many engineer devices,such as lift elevator,cableway,conveyor belt,etc.The transverse vibration problem of these common engineering equipment seriously affect the use of the effect and the safety.So the research of the transverse vibration problem of axially travelling string system is necessary.In this paper,axially travelling string system is researched.Firstly,the simplified dynamic model of axially travelling string system is proposed.Based on Hamilton principle,the dynamic equations of axially travelling string system is established.Secondly,based on the finite technique,the corresponding method for transverse vibration response of axially travelling string system is proposed and the energy calculation method of axially travelling string system is solved.Then,the problem of natural frequency of axially travelling string system with constant and variable length is investigated by the vibration period and natural mode of transverse wave on the string.The difference of natural frequency of axially travelling string between constant and variable length is obtained.The relationship of natural frequency and axial speed for different values of tension is studied.Finally,boundary damping control law of the transverse vibration of axially travelling string system is studied by applying a damping device at the ends of axially travelling string system.The amplitude ratio of reflected wave to incident wave is investigated by the force equilibrium principle at the boundary condition.The energy ratio of reflected wave to incident wave is investigated by the energy equation.According to the amplitude reflection ratio and the energy reflection ratio,the boundary control function are obtained.Damping coefficient and the optimal value are obtained by the boundary control function.So the purpose of transverse vibration control of axially travelling string system is achieved.The research provides a theoretical basis for the design and the analysis of axially travelling devices in engineering.