随机窄带参激下二自由度非线性系统  

Two-degree-of-freedom Nonlinear System in Narrow-band Random Excited

作　　者：贺群[1] 徐伟[2] 戎海武[3] 方同[2] 

机构地区：[1]武警工程学院,西安710086 [2]西北工业大学,西安710072 [3]佛山大学,佛山528000

出　　处：《应用力学学报》2002年第4期122-125,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金 (10 0 72 0 49)资助

摘　　要：研究了带平方二自由度非线性系统在随机窄带参数激励下 ,用多尺度法分离了系统的快变项 ,讨论了系统的各参数对响应的影响。在一定条件下 ,系统具有两个均方响应值 ,具有跳跃现象和饱和现象 ,数值模拟表明提出的方法是有效的。The two to one internal resonance and the principal resonance of a two degree of freedom nonlinear system to narrow band random parametric excitation are investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior and stability of steady state response are studied by means of qualitative analyses. The effects of bandwidth and magnitudes of deterministic and random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the intensity of the random excitation increase, the nontrivial steady state solution may change form a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions, and saturation and jumps may exist.

关 键 词：二自由度参数激系统 窄带激励 2:1内共振 主共振 多尺度法 饱和 跳跃 

分 类 号：TB114.2[理学—运筹学与控制论] O324[理学—概率论与数理统计]