多自由度非線形振動系の内部共振 : 固有振動数がp_1+p_2=p_3および2p_1+p_2=p_3の関係を満たす場合

概要

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The characteristics of oscillations induced in a nonlinear vibratory system whose natural frequencies are not in the ratio of prime integers and yet satisfy the condition of internal resonance, are discussed via a typical example. The example taken up here is a three-degree-of-freedom system whose linearized natural frequencies p_i (i=1, 2, 3, ; p_1<p_2<p_3) satisfy the condition p_1+p_2=p_3 or 2p_1+p_2=p_3, and which is subjected to harmonic excitation. The characteristics of oscillations induced in the system near primary as well as secondary resonance points are examined. For analysis, the harmonic balance method is employed. The analysis reveals that near some of the resonance points, internal resonance occurs accompanying three harmonics of frequencies satisfying a certain relation. Also shown is that an almost periodic motion can occur. The validity of the obtained results is checked by performing direct numerical integration.
一般社団法人日本機械学会の論文
1986-02-25