多自由度非线性振动系统的内共振
On Internal Resonance of Nonlinear Vibrating Systems with Many Degrees of Freedom
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Abstract: The problem of periodic solutions of nonlinear autonomous systems with many degrees of freedom is considered.This is made possible by the development of a modified version of the KBM method[1].The method can be used to generate limit cycle phase portrait,amplitude,period and to indicate stability of the limit cycle.
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Key words:
- nonlinear oscillations /
- phase-locked solution /
- phase portrait
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[1] Bogoliubov,N.N.,and J.A.Mitropolsky,Asymptotic Methods in the Theory of Nonlinear Vibrations,Moscow,Nauka(1974). [2] Navfeh.A.H.,and D.T.Mook.Nonlinear Osciltations,Wiley,New York(1979). [3] Mickens,R.E.,A regular perturbation technique for nonlinearly coupled oscillators in resonance,Journal ofSoundand Vibration,81(1982),307-310. [4] Sptysl,H.,Internal resonance of non-linear autonomous vibrating system with two degrees of freedom,Journal of Sound and Vibration,112(1987),63-67. [5] Xu Zhao and Zhang Ling-qi,Asymptotic method for analysis of non-linear systems with two parameters,Acta Mathematica Scientia,6(1986),453-462. [6] Pavlidis,T.,Biological Oscillators:Their Mathematical Analysis,Academic Press,New York(1973). [7] Rand,R.H.,and P.J.Holmes,Bifurcation of periodic motions in two weakly coupled van der Poi oscillators,Int.J.Non-Linear Mechanics,15(1980),387-399. [8] Lau.S.L.,Y.K.Cheung and S.Y.Wu,A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems,ASME.J.Appl.Mech.,49(1982),849-853. [9] Xu Jian-xue,R.S.Guttalu,and C.S.Hsu,Domains of attraction for multiple limit cycles of coupled van der Poi equations by simple cell mappings,Int.J.Non-Linear Mech.,20(1985),507-517.
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