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。
The physical models of an axially travelling string system with time- varying length under the action ofmoving concentrated load and moving distributed load are established. Two kinds of moving forced string models areconsidered with different means. The nonlinear transversely forced vibration equations with time varying parameters of thestring under different conditions are derived using the extended Hamilton’s principle and Leibniz’s rule, and discretizedusing different order Galerkin method into a series of ordinary differential equations. The modified 4th-order Runge-Kuttamethod is employed to solve the nonlinear transverse vibration equations by means of Matlab code. The numerical resultsalso obtained by the Newmark- β method based on finite element analysis. The effects of parameters changing with themoving loads are also simulated. The results demonstrate the correctness of the proposed physical and mathematical modelsand the effectiveness of the solutiion methods with time varying parameters. It also indicates that the proper choosing ofGalerkin truncation order can achieve better convergence and calculation accuracy in different situations.
出处
《噪声与振动控制》
CSCD
2016年第3期16-20,56,共6页
Noise and Vibration Control
基金
国家自然科学基金资助项目(51305115)
