随机及移动荷载激励下弹性梁分岔与混沌  

BIFURCATION ANDCHAOS OF BEAM SUBJECTED TO MOVING LOADS AND RANDOM EXCITATIONS

作　　者：李海涛[1] 秦卫阳[1] 田瑞兰[2] 

机构地区：[1]西北工业大学工程力学系 [2]石家庄铁道大学数理系

出　　处：《动力学与控制学报》2015年第6期418-423,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11272257;11172234)~~

摘　　要：移动荷载通过简支梁时,粗糙的梁表面会使移动荷载转变为随机激励.本文考虑梁的几何非线性因素,基于随机Melnikov理论确定了系统在均方意义下发生异宿分岔以及混沌的边界条件.利用数值随机Runge-Kutta方法对随机激励和周期激励共同作用下的系统响应进行了仿真计算,最大Lyapunov指数等数值结果描述了动力学行为变化过程.结果表明当荷载的速度一定时,梁跨中的非线性动力学行为受到质量和随机激励的共同影响,表面平整度较差的梁会增加混沌产生的可能性.moving loads pass through the rough surface of beam. Considering the characteristics of random excitation, present nonlinear model of moving loads different beam roughness. The critical condition in of mean square is obtained by random Melnikov process. The response of structure under the combin of random and periodic excitation is simulated, and used to the variation of dynamic behaviors. It is concluded that speed, nonlinear dynamic behaviors mid-span of beam are severely influenced by the random excitation. Therefore poor flatness of surface would increase the probability of occurrence of chaos.

关 键 词：表面平整度 移动荷载 随机Melnikov过程 混沌 

分 类 号：U441.2[建筑科学—桥梁与隧道工程]