Effects of anisotropic supports on the stability of parametrically excited slender rotors

This study is aimed at investigating the effects of anisotropic supports on the stability of slender rotors parametrically excited by external loads. An axisymmetric shaft described by scaling a spinning Timoshenko beam on anisotropic supports is studied, loaded by oscillating axial end thrust and twisting moment, with the possibility of carrying additional inertial elements like discs, which represents a model including all the general features of slender rotors which are relevant for this kind of stability analysis, gyroscopic effects comprised. Stability is studied after discretization of the equations of motion into a set of coupled ordinary differential Mathieu-Hill equations. The influence on stability of angular speed combined with anisotropy in the supports (including principal stiffness, principal damping and cross-elements) is analysed with respect to frequency and amplitude of the external loads on stability charts in the form of Ince-Strutt diagrams. The occurrence of different kinds of critical solutions, simple and combination, is investigated, highlighting their dependency on both the degree of anisotropy in the supports and angular speed.