Research On Numerical Methods For Solving Transverse Vibration Of Axially Travelling String And Parametric Vibration

Axially travelling string system represents many engineer devices, noise and vibrations of these devices, especially transverse vibrations have limited their applications. Therefore, i the transverse vibration of axially travelling string system is important for the design of the device. This paper is supported by the National Natural Science Fund Project "research on parametric vibrations of axially travelling string system with time varying degrees of freedom and experiment"(No.51305115).In this paper, axially travelling string system is researched, firstly, the simplified dynamic model of axially travelling string system is established, the finite element technique on the basis of time varying degrees of freedom is applied to expand the use of Hamilton principle to establish the dynamic equations of the system. Secondly, the corresponding methods for solving linear dynamic equations and nonlinear dynamic equations of axially travelling string system are proposed, transverse vibration response of the system is solved and the function of the nonlinear term of the dynamic equation is analyzed. Then, the method of calculating the energy of the finite element discrete system is researched, as well as the energy changes during the string length retraction and extension and energy transfer mechanism of the travelling string at a boundary; parametric vibration of the system such as the critical speeds natural frequency and modal vibration is solved. Finally, the practical application of axially travelling string system is presented. The vibration control problem of an axially travelling string system with damping device is considered, dynamic characteristic of flexible moving belt and transverse vibration characteristic of viscoelastic warp of high speed loom are analyzed. The research provides a theoretical basis for the design of axially travelling devices in engineering.