Internal Resonance in a Nonlinear Multi-degree-of-freedom Vibratory System When Its Natural Frequencies Satisfy the Condition p_1+p_2=p_3 or 2p_1+p_2=p_3

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概要

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• The characters of oscillations induced in a nonlinear vibratory system whose natural frequencies are not in the ratios 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 of 2p_1 + p_2 = p_3, and which is subjected to harmonic excitation. The characters 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 the internal resonance occurs accompanied with three harmonics with their frequencies satisfying a certain relation. With three harmonics with their frequencies satisfying a certain relation. Also it is shown that an almost periodic motion can occur. The validity of the obtained results is confirmed by direct numerical integration.

• 一般社団法人日本機械学会の論文

著者

• Yamamoto Toshio

  Faculty Of Engineering Nagoya University

• Kato Masayoshi

  School Of Engineering Nagoya University

• Yasuda Kimihiko

  School Of Engineering Nagoya University

• Yamamoto Toshio

  Faculty Of Science And Technology Meijyo University

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