关键词: 振动与波；时变长度移动绳；Galerkin法；Newmark-&beta, 法；移动载荷；横向受迫振动

Abstract:

The physical models of the axial travelling string system with time-varying length under the action of moving concentrated load and moving distributed load is established. Two kinds of moving forced string models are considered with different means. The nonlinear transverse forced vibration equations with time varying parameters of the string under different conditions are derived using the extended Hamilton's principle Leibniz's rule, and discretized using different order Galerkin method into a series of ordinary differential equations. The modified Fourth-order Runge_Kutta method is presented to solve the nonlinear transverse vibration equations based on Matlab numerical simulations. The numerical results also obtained by the Newmark_beta method based on finite element discretization. The effects of changing different parameters with the moving force are also simulated. The results demonstrate the correctness of the proposed physical and mathematical models, the effectiveness of the solving methods with time varying parameters. It also indicates that the proper choosing of Galerkin truncation order can achieve better convergence and calculation accuracy under different situations.