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《Acta Mechanica Sinica》 2005-01

## ON INTERNAL RESONANCE OF NONLINEAR VIBRATION OF AXIALLY MOVING BEAMS

Chen Shuhui~2) Huang Jianliang (Department of Applied Mechanics and Engineering,Zhongshan University,Guangzhou 510275,China)
In this paper,the multiple dimensions Lindstedt-Poincaré method is formulated for analysis ofnonlinear vibration with internal resonance of axially moving beams.Firstly,the governing equations of anaxially moving beam are derived through Hamilton's principle.Then the Galerkin method is used to discretizethe governing equations.After that the separated equations are solved by the multiple dimensions L-P method.The discriminant of the frequency-amplitude equation is derived.The detailed theoretical analysis reveals thatthe forced responses with internal resonance are excitation-level dependent.The critical value of the forced am-plitude can be determined theoretically.Numerical results show the complicated frequency-amplitude responsecurves of forced vibration with internal response and reveal the rich and interesting nonlinear phenomena.Thenumerical results of the multiple dimensions L-P method are identical with those of IHB method when thevibration with small amplitude.
【Fund】： 国家自然科学基金(10272117) 广东省自然科学基金(011203) 中山大学高等学术研究中心基金(04M6)．~~
【CateGory Index】： O322
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