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.
出处
《工程力学》
EI
CSCD
北大核心
2006年第6期50-53,59,共5页
Engineering Mechanics
关键词
弹性直杆
热膨胀
非线性振动
转迁集
分岔
elastic straight bar
thermal expansion
nonlinear vibration
transition variety
bifurcation
