Primary and combined multi-frequency parametric resonances of a rotating thin-walled composite beam under harmonic base excitation

Abstract

A clamped rotating thin-walled composite elastic blade subjected to periodic base excitation is considered in this paper. The mathematical model of the structure captures the complex coupled bending–shear–torsional deformations of the beam resulting from the layout of the composite material. The partial differential equations of motion are formulated based on the Hamilton’s principle and next discretized according to the Galerkin’s method. The coefficients of the final state equations are found to be time dependent and have two distinct frequencies, namely the base excitation and the angular velocity of the system. The derived and initially coupled set of governing equations of motion is uncoupled and the method of multiple time scales is used to determine the transition lines separating stability regions of the system on Ince-Strut diagram. Numerical results are presented to illustrate the influence of the composite reinforcing fibres orientations as well as rotating speed and base excitation frequency on the dynamic stability of the structure.