Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

Abstract

AbstractIn this article, nonlinear nonstationary vibration of a rotating composite shaft passing through critical speed excited by non‐ideal energy source is investigated. Geometrical nonlinearity, gyroscopic effect, rotary inertia and coupling due to material anisotropy are considered, while shear deformation is neglected. By using Hamilton principle, axial‐flexural‐flexural‐torsional‐rotational equations of motion for a composite shaft with variable rotational speed are derived. External source is assumed as non‐ideal that causes the interaction between external torque and vibrating system. To obtain the approximate analytical solution, perturbation theory (multiple scales method) is applied to reduce the equations in the neighborhood of the first critical speed. Although, the analysis is done for the first critical speed, one‐mode discretization is not enough. Indeed, at least two modes is required to obtain accurate results. The effects of external damping, eccentricity, angle of fibers, resistive torque, nonlinear terms, and also the effect of the extensional–torsional coupling on occurrence of Sommerfeld effect are investigated. It is shown that nonlinearity and coupling possess significant effect on the prediction of Sommerfeld phenomenon. Moreover, as observed, with appropriate implementation of layup and stacking sequence, one can obtain the best performance for the nonstationary behavior of composite shaft.