Stability and bifurcation of a rotating blade with varying speed

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Shaid Bahonar University of Kerman

2 Department of Mechanical Engineering, Sirjan University of Technology

3 Department of mechanical engineering,Shahid Bahonar University of Kerman, Kerman,Iran

Abstract

In this paper, the nonlinear vibration of a rotating blade with varying rotating speeds is investigated. The rotating blade is considered as a rotating cantilever Euler-Bernoulli beam without geometric nonlinearity. The angular velocity is assumed as a constant value which is fluctuated with small amplitude. The nonlinear partial differential equations of the rotating cantilevered beam are derived in three-dimensional using Hamilton's principle. Then, the Galerkin discretization method is applied to the nonlinear partial differential equations to obtain three nonlinear ordinary differential equations. The method of multiple scales is utilized to derive six first-order ordinary differential equations to describe the time variation of amplitudes and phases of interacting modes. The stability and bifurcation of fixed points are obtained by using the eigenvalues of the Jacobian matrix of the modulation equations. Numerical results demonstrated that near the primary resonance and internal resonance the fixed points lose the stability through the saddle node bifurcation. Moreover, the transfer energy among the modes and jump in amplitude of modes occur in frequency response at the different cases of internal resonance.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 4 (Special Issue)
July 2021
Pages 2459-2472

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