Internal Resonance in a Nonlinear Multi-degree-of-freedom Vibratory System When Its Natural Frequencies Satisfy the Condition p<SUB>1</SUB>+p<SUB>2</SUB>=p<SUB>3</SUB> or 2p<SUB>1</SUB>+p<SUB>2</SUB>=p<SUB>3</SUB>

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Description

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 pi (i=1, 2, 3; p1 < p2 < p3) satisfy the condition p1 + p2 = p3 of 2p1 + p2 = p3, 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.

Journal

  • Bulletin of JSME

    Bulletin of JSME 29 (256), 3468-3475, 1986

    The Japan Society of Mechanical Engineers

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