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.

摘要：

分别建立移动集中载荷和移动分布式载荷作用下时变长度轴向移动绳系统的物理模型，基于Leibniz 法和Hamilton 原理推导具有时变参数的横向受迫振动方程，Galerkin法将其离散处理为一系列非线性常微分方程组，改进的四阶Runge-Kutta用于求解不同Galerkin截断阶数的非线性常微分方程组，同时分析基于有限元法求解系统运动方程及Newmark-β数值计算的移动集中载荷下变长度轴向移动绳系统横向振动特性。两种方法数值分析吻合性及收敛性表明建立变长绳移系统模型可靠性及求解时变参数系统方法有效性，同时变长度轴向移动绳系统在不同情况下采用恰当的Galerkin截断阶数能到达更好收敛性及保证计算精度。

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