Stability and Bifurcation of a Continuum Rotor with Transverse Electromagnetic and Bearing Excitations
This paper presents the stability and bifurcation of a continuum rotor with transverse electromagnetic and bearing excitations. The rotor system is modeled as continuous beam which is excited by uniformly distributed electromagnetic force and two oil-film forces. Using the Galerkin’s method, the partial differential equation of nonlinear motion is discretized as second order ordinary differential equations. The harmonic balance method is used to determine the approximate periodic solution, then the Floquet multipliers are obtained and the stability of periodic solution can be judged. The Andronov-Hopf bifurcation is presented when the leading Floquet multiplier continually changing with rotation speed passes the unit circle on the complex plane. Bifurcation diagrams of displacement with varying rotation speed are obtained using the Runge-Kutta method. Periodic motion and quasi-periodic motions appear alternately with the rotation speed showing inherent interaction between electromagnetic force and oil-film forces.
Paul P. Lin and Chunliang Zhang
H. Y. Luo and Y. F. Wang, "Stability and Bifurcation of a Continuum Rotor with Transverse Electromagnetic and Bearing Excitations", Applied Mechanics and Materials, Vols. 105-107, pp. 439-443, 2012