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Two-mode combination resonances of an in-extensional rotating shaft with large amplitude

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Abstract

In this paper, two-mode combination resonances of a simply supported rotating shaft are investigated. The shaft is modeled as an in-extensional spinning beam with large amplitude. Rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The equations of motion are derived with the aid of the Hamilton principle and then transformed to the complex form. The method of harmonic balance is applied to obtain analytical solutions. Frequency-response curves are plotted for the combination resonances of the first and the second modes. The effects of eccentricity and external damping are investigated on the steady state response of the rotating shaft. The loci of saddle node bifurcation points are plotted as functions of external damping and eccentricity. The results are validated with numerical simulations.

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Authors and Affiliations

  1. P.O. Box 14115-177, Tehran, Iran

    S. E. Khadem

  2. Department of Mechanical Engineering, Tarbiat Modarres University, Tehran, Iran

    S. E. Khadem, M. Shahgholi & S. A. A. Hosseini

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  1. S. E. Khadem
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  2. M. Shahgholi
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  3. S. A. A. Hosseini
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Correspondence to S. E. Khadem.

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Khadem, S.E., Shahgholi, M. & Hosseini, S.A.A. Two-mode combination resonances of an in-extensional rotating shaft with large amplitude. Nonlinear Dyn 65, 217–233 (2011). https://doi.org/10.1007/s11071-010-9884-2

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  • DOI: https://doi.org/10.1007/s11071-010-9884-2

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