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Principal resonance of a nonlinear system with two-frequency parametric and self-excitations

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Abstract

The principal resonance of a single-degree-of-freedom system with two-frequency parametric and self-excitations is investigated. In particular, the case in which the parametric excitation terms with close frequencies is examined. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. Qualitative analyses are employed to study the behaviour of steady state responses, limit cycle responses and 2-torus responses, including their stability and bifurcation. The effects of damping, detuning, and magnitudes of self-excitation and parametric excitations are analyzed. The theoretical analyses are verified by numerical integration results of the governing equation and the modulation equations.

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Author notes

  1. O. S. Lu

    Present address: Department of Applied Mathematics and Physics, Beijing University of Aeronautics and Astronautics, 100083, Beijing, China

Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Western Ontario, N6A 5B9, London, Ontario, Canada

    O. S. Lu & C. W. S. To

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  1. O. S. Lu
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  2. C. W. S. To
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Lu, O.S., To, C.W.S. Principal resonance of a nonlinear system with two-frequency parametric and self-excitations. Nonlinear Dyn 2, 419–444 (1991). https://doi.org/10.1007/BF00045437

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  • DOI: https://doi.org/10.1007/BF00045437

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