Further insights in the dynamic analysis of parametrically excited stable rotors with unbalance: shear and gyroscopic effects.

This study, following a previous investigation by the same authors, deals with unbalance effects in the stable domain of a slender rotor parametrically excited by an axial end thrust, considering in addition, as a novel contribution, the effects of shear deformation and gyroscopic actions. Unbalance causes a harmonic load acting on flexural deflection, influencing the response together with the parametric excitation, yielding a sequence of combination external resonances, also affecting the critical speeds of the rotor. A distributed-parameter model is adopted, consisting of a homogeneous Euler-Bernoulli straight beam spinning at constant angular speed on isotropic supports, unbalanced and loaded by an axial end thrust with a harmonic time-dependent component. Shear deformation and gyroscopic effects are studied separately, by considering additional terms in the Euler-Bernoulli model, either the Euler-Bernoulli beam model plus shear or the Rayleigh beam model. The flexural response is investigated in the frequency domain by decoupling the dynamic equilibrium equations in exact and approximate forms, yielding scalar non-homogeneous Mathieu equations.