车桥耦合系统的近似解研究  

Research of Approximate Solutions for Vehicle-bridge Coupled Vibration System

作　　者：郭秀英[1] 吴启亮[1] 李海涛[1] 

机构地区：[1]石家庄铁道大学数理系,河北石家庄050043

出　　处：《石家庄铁道大学学报（自然科学版）》2014年第1期1-8,共8页Journal of Shijiazhuang Tiedao University(Natural Science Edition)

基　　金：国家自然科学基金(11002093);石家庄铁道大学科研启动金(Q21)

摘　　要：采用GSB方法研究车桥耦合模型一些特殊情况下的近似解。针对车桥耦合模型,由Lagrange方程得到了变刚度SD振子的动力学方程。利用GSB方法对μ(t)作为常数激励的情况进行讨论,得到了非对称系统的含有完全椭圆积分的二阶近似解表达式。利用Matlab进行数值模拟,并将近似结果与原系统进行比较,发现近似解与原系统十分接近。In order to research the approximate solutions for vehicle-bridge coupled vibration, we established a vehicle-bridge coupled model, and obtained the dynamic equations of the variable stiffness SD oscillator with the Lagrange equation. We discussed the situations that the parameter is a constant excitation by GSB perturba- tion technique respectively. Finally, we obtained the expression of the second-order approximate solution of the asymmetric system which contains the complete elliptic integral. The approximate solution has been compared with the exact solution of original system with the help of MATLAB numerical stimulation tools, and it is found that the result is approximate to the original system.

关 键 词：非线性振动 SD振子 GSB方法 车桥耦合系统 椭圆积分 

分 类 号：O322[理学—一般力学与力学基础]