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Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

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Abstract

The modal interaction which leads to Hamiltonian Hopf bifurcation is studied for a nonlinear rotating bladed-disk system. The model, which is discussed in the paper, is a Jeffcott rotor carrying a number of planar blades which bend in the plane of the motion. The rigid rotating disk is supported on nonlinear bearings. It is supposed that this dynamical system is a Hamiltonian system which is perturbed by small dissipative and nonlinear forces. Krein’s theorem is employed for obtaining a stability criterion. The nonlinear eigenvalue equations on the stability boundary are turned into ordinary differential equations (ODEs) by differentiating them over the rotating speed. By solving these ODEs, the eigenmodes and the eigenvalues on the stability boundary are obtained. The bifurcation analysis is performed by applying multiple scales method around the boundary. The rotor nonlinear behavior and damping effects are studied for different conditions on the rotating speed and nonlinearity type by the bifurcation equation. It is shown that the damping distribution between the blades and bearings may shift the unstable mode. Depending on the nonlinearity type, subcritical and supercritical Hopf bifurcation are possible.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

    Asghar Najafi & Mohammad-Reza Ghazavi

  2. Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Ali-Asghar Jafari

Authors
  1. Asghar Najafi
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  2. Mohammad-Reza Ghazavi
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  3. Ali-Asghar Jafari
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Correspondence to Mohammad-Reza Ghazavi.

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Najafi, A., Ghazavi, MR. & Jafari, AA. Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor. Nonlinear Dyn 78, 1049–1064 (2014). https://doi.org/10.1007/s11071-014-1495-x

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  • DOI: https://doi.org/10.1007/s11071-014-1495-x

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