近接した固有振動数をもつ二自由度非線形系の強制振動(機会力学,計測,自動制御)

概要

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This paper deals with nonlinear forced oscillations in a two-degree-of freedom system in which natural frequencies are comparatively close. Two kinds of approximated differential equations for amplitudes and phase angles of a harmonic oscillation and of a combination resonance are derived. The resonance curves and their stability analyses, and the local bifurcation analysis are made by using these equations. The numerical simulation analyses are performed to obtain time histories, their spectra, Poincare maps and Lyapunov exponents by using the original equations of motion. As a result, it is found that Hopf bifurcations can occur on the branch of the resonance curves for the harmonic oscillation, and that chaotic vibrations may occur after the appearance of a period doubling bifurcation, which are generated from the Hopf bifurcation point. The differences of the accuracy between these two kinds of approximated differential equations are also discussed.
社団法人日本機械学会の論文
2002-09-25