Research On Modeling And Transverse Vibration For An Axially Travelling String System Under External Load

The transverse vibration of many axially travelling string systems can be simplified as a study of the free transverse vibration, there are also many other systems must be simplified as a research on the forced transverse vibration under moving concentrated load, moving distributed load and boundary load respectively. For example, the cable crane under wind load, the transmission cable with a moving pulley, uneven density or abrasion lead to uneven quality of the travelling string system, the boundary load which is caused by the uneven of the two ends support etc. Therefore, the research on the free and forced transverse vibration characteristics of the axial moving string is very important to the design and reform and vibration control of equipments.The axially travelling string system is studied in this thesis. Firstly, the physical models of axially travelling string systems under moving concentrated load, moving distributed load and boundary load are established respectively, the solving methods of different types of mathematical models also are studied, the transverse vibration equations of the string under different conditions are derived using the Hamilton principle.Secondly, the different order Galerkin method is implemented to transform the nonlinear partial differential equation into a series of ordinary differential equations. The finite element technique on the basis of time-varying degrees of freedom is adopted with Lagrange’s equation to establish the dynamic equations of the system.Then, the modified Fourth-order Runge-Kutta method is presented to solve the transverse nonlinear vibration equations based on Matlab numerical simulations.. The numerical results compared with the Newmark-beta method based on finite element discretization. The results demonstrate the correctness and effectiveness of the proposed mathematical models and solving methods. It also indicates that the proper choosing of Galerkin truncation order can achieve better convergence under different load.Finally, the influence of the different parameters on the transverse vibration of the axially travelling string is studied, and the comparison with the vibration characteristics of the axially travelling string under moving concentrated load and moving load are analyzed. Two examples are given in the actual engineering applications, which have the important theoretical and practical significances of the research with modeling and vibration of axially string under external load.