Chaos and bifurcation in nonlinear in-extensional rotating shafts

In this paper, bifurcation and chaotic behavior of in-extensional rotating shafts are investigated. The shaft is modeled as a Rayleigh simply supported beam, spinning with constant rotational speed. Using two–mode Galerkin truncation, the partial differential equations of motion are discretized and then with the aid of numerical simulations, the dynamical behavior of the rotating shaft is studied. Using tools from nonlinear dynamics, such as time history, bifurcation diagram, Poincaré map, Lyapunov exponents, and amplitude spectra, a comprehensive analysis is made to characterize the complex behavior of the rotating shaft. Periodic (synchronous), quasi-periodic, chaotic and transient chaotic responses are observed in the neighborhood of the second critical speed. The effect of rotary inertia and damping on the dynamics of the rotating shaft is considered. It is shown that the chaotic response is possible for a shaft with weak nonlinearity without the existence of any internal resonance.