基于突变理论的异型拱桥非线性动力失稳研究  

Research on Dynamic Instability of Irregularly - shaped Arch Bridge Based on Catastrophe Theory

作　　者：杨晓蓉[1] 郑治国[1] 韩天石[2] 孟泉[1] 蔺金太[1] 

机构地区：[1]军事交通学院基础部,天津300161 [2]军事交通学院汽车指挥系,天津300161

出　　处：《军事交通学院学报》2009年第2期85-90,共6页Journal of Military Transportation University

摘　　要：根据异型拱桥——柳林桥大V梁横向刚度差这一特点,基于突变理论提出了大V梁的横向动力失稳分析模型。对影响大V梁的稳定的机理进行了分析,给出了两个尖点的坐标G1（η1,μ1）,G2（η2,μ2）以及大V梁稳定与不稳定的分叉点集。分析了非线性系数μ和频率比η=Ω/ω=1这两个参数对大V梁振幅的影响,提出当大V梁的非线性系数μ〉η2时,η在一定范围的连续变化会引起振幅的突然的跳跃变化,也即产生跳跃现象,结论表明这种现象会对大V梁造成失稳破坏。According to the characteristic of poor stiffness of V - shaped beams, transverse dynamic instability model of V - shaped is presented by Catastrophe Theory, mechanism of stability of V - shaped is analyzed, coordinates of two cusps G1 （η ,μ1 ）, G2 （η2,μ2 ）and instable bifurcation set is derived. Effect of nonlinear coefficient μ and frequency ratio η= Ω/ω = 1 on amplitude of V - shaped beams are analyzed. When nonlinear coefficient μ is equal to 0, V - shaped beams behave as a linear oscillator and its amplitude have maximum at η= Ω/ω = 1 of resonance. When nonlinear coefficient is 0 〈μ 〈 η2, continuous change of η can not arise abrupt change of amplitude. When nonlinear coefficient is μ 〈η2, continuous change of η can arise abrupt change of amplitude, then the jumping phenomenon can lead destruction of V - shaped beams.

关 键 词：异型拱桥 大柔度桥梁 横向非线性受迫振动 突变理论 动力失稳 

分 类 号：TU311.2[建筑科学—结构工程]