二自由度非線形系の内部共振現象 : 第2報,固有振動数比が1:2で共振点の重なりがない和差・超和差調波振動

概要

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The influences of the internal resonance on the summed-and differential harmonic oscillation [p_1+p_2] and the ultra-summed-and-differential harmonic oscillation [(p_1+p_2)/2] in a nonlinear two-degree-of-freedom system whose natural frequencies, p_1 and p_2, are at the ratio of 1:2 are discussed. The resonance points of these oscillations do not coincide with those of other kinds of oscillations. These are the oscillations whose coexisting components do not have the frequency ratio of an integer when the relationship of internal resonance does not hold. In this paper, we investigated the relating nonlinear components, the variations in the shape of resonance curves, the change in the stability of the stationary solutions, the occurrence of the almost periodic oscillations, and the occurrence of new stationary oscillations by theoretical analysis. In the results, it is clarified that, due to the influence of the internal resonance, (a) other kinds of nonlinear components become influential, (b) the stationary oscillations which are observed in a system with no internal resonance change to almost periodic oscillations, and (c) stationary oscillations whose vibration components are at the frequency ratio of an integer become apparent.
社団法人日本機械学会の論文
1989-08-25