密集模态响应饱和与线性模型失效研究  

Study of the Linear Model Efficiency When Response Saturation Existing With Closely Spaced Natural Frequencies

作　　者：白鸿柏[1] 郑坚[1] 张培林[1] 陈振藩[2] 

机构地区：[1]军械工程学院兵器工程系,石家庄050003 [2]南京航空航天大学,南京210016

出　　处：《机械科学与技术》2001年第2期227-228,230,共3页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金! (193 72 0 2 4);航空基金! (94B5 2 0 10 )

摘　　要：通过对一两自由度密频近线性系统主共振响应分析 ,揭示了由于密频内共振的存在 ,密集模态坐标的运动将产生复杂的非线性响应饱和现象 ,此时 ,线性模型失效 ,必须采用非线性模型 ;同时 ,讨论了线性模型失效与激励强度、系统初始条件的依赖关系。In this paper, by analyzing principal resonance of a two-degree-of-freedom nearly linear system with closely spaced natural frequencies using the average method in the nonlinear vibration theory, the conclusion that typical response saturation nonlinear kinetic phenomena would happen when IRCF (internal resonance clue to closely spaced natural frequencies) exists was obtained. It is shown that while excitation level is very small, the trivial solution is only stable one, in first-order approximation, the linear model is still effective. A deep investigation shows that while excitation level is stronger or moderate, the response modes will be very complicated. If trivial solution loses stability, at the same time, the saturation solution is only stable one, and then the linear model will no longer be effective. If the trivial solution and the saturation solution or the trivial solution and almost periodic motion caused by the saturation solution losing stability due to occasionally existing of the hopf bifurcation, in this case, the losing effectiveness of the linear model will relate to the initial conditions.

关 键 词：非线性振动 密频内共振 主共振响应 密集模态 

分 类 号：O322[理学—一般力学与力学基础] O328[理学—力学]