%0 Journal Article
%T BIFURCATION OF NONLINEAR NORMAL MODES OF MULTI-DEGREE-OF-FREEDOM SYSTEMS WITH INTERNAL RESONANCE<br>多自由度内共振系统非线性模态的分岔特性
%A Lin Xinye Chen Yushu Wu Zhiqiang Chen Fangqi
%A <br>李欣业
%A 陈予恕
%A 吴志强
%A 陈芳启
%J 力学学报
%D 2002
%I 
%X The method of multiple scales is applied for constructing nonlinear normal modesof a three-degree-of-freedom system which is discretized from a two-link flexible arm connectedby a nonlinear torsional spring. The discrete system is with cubic nonlinearity and 1:3 internalresonance between the second and the third modes. The approximate solution for the nonlinearnormal modes associated with internal resonance are presented. The NNMs determined here tendto the linear modes as the nonlinearity vanishes, which is significant for one to construct nonlinearnormal modes. Greatly different from results of those nonlinear systems without internal resonance,it is found that the nonlinear normal modes involved in internal resonance include both coupled anduncoupled kinds. The bifurcation analysis of the coupled NNM of the system considered is givenby means of the singularity theory The pitchfork and hysteresis bifurcation are simultaneouslyfound. Therefore, the number of nonlineax normal modes arising from the internal resonance mayexceed the number of linear modes, in contrast with the case of no internal resonance, wherethey are equal. Curves displaying variation of the coupling extent of the coupled NNM with theinternal-resonance-deturing parameter are proposed for six cases.
%K multiple-degree-of-freedom system
%K internal resonance
%K nonlinear normal modes
%K mode coupling
%K mode bifurcation<br>多自由度系统
%K 内共振
%K 非线性模态
%K 模态耦合
%K 模态分岔
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=37402575A08971AB&yid=C3ACC247184A22C1&vid=339D79302DF62549&iid=38B194292C032A66&sid=238BD7580EFCC5AE&eid=8CCD0401CC9AE432&journal_id=0459-1879&journal_name=力学学报&referenced_num=5&reference_num=19