弹性直杆在温度场中的非线性振动与奇异性  

SINGULARITIES AND NONLINEAR VIBRATION OF ELASTIC STRAIGHT BARS IN THERMAL FIELD UNDER HARMONIC EXCITATION

作　　者：杨志安[1] 席晓燕[2] 李文兰[3] 

机构地区：[1]唐山学院唐山市结构与振动工程重点实验室,唐山063000 [2]河北理工大学机械工程学院,唐山063000 [3]天津大学图书馆,天津300072

出　　处：《工程力学》2006年第6期50-53,59,共5页Engineering Mechanics

摘　　要：由伽辽金方法得到了弹性直杆热胀冷缩状态下受均布简谐激励的非线性振动方程。应用多尺度法求得了系统主共振的分岔方程和不同参数下的主共振响应曲线。随着温度的降低,主共振幅频响应曲线的振幅增加,共振区变窄。得到了主共振温度响应曲线的两种拓扑结构及其变化趋势。按照奇异性理论方法对主共振分岔方程进行了分析,得到了分岔方程的转迁集和分岔图。The nonlinear vibration equation of the elastic straight bar under thermal expansion and harmonic excitation is obtained by Galerkin principle. The bifurcation equation of the primary resonant of the system is acquired by the method of multiple scales. The primary resonant response curves are analyzed. With the temperature decreasing, amplitudes of response curves increase and the resonant regions shrink. The temperature response curves of the system have two kinds of topological structures. By means of singularity theory the transition variety and bifurcation diagram of the bifurcation equation of the system is acquired.

关 键 词：弹性直杆 热膨胀 非线性振动 转迁集 分岔 

分 类 号：O322[理学—一般力学与力学基础]