PRIMARY RESONANCES OF AN INTERNALLY DAMPED ROTATING COMPOSITE SHAFT WITH NONLINEARITIES IN CURVATURE AND INERTIA

The rotating shaft made of anisotropic composites is a class of typical rotor dynamic system which has a wide application in the structural design of advanced helicopter power transmission and automotive drive system. The nonlinear rotordynamic behavior study of these system has significance in theory and practice. However, at present, the research about nonlinear dynamic of rotordynamic system has restrainedly been the rotating isotropic shaft, and the effect of internal material damping is seldom considered. In this paper, the primary resonances of an internally damped rotating composite shaft are investigated. Nonlinearity comes from curvature and inertia induced by large deformation of in-extensionality composite shaft. Internal material damping comes from the dissipative properties of viscoelastic composite. The dynamical model incorporates rotary inertia and gyroscopic effect. The extended Hamilton principle is employed to derive the nonlinear equations of bending-bending vibration of rotating composite shaft. The Galerkin method is used to discretize these nonlinear equations, and the multiscale method is adopted to perturbtion analysis the ordinary differential equation, then the analytical expression of primary resonances are derived. The internal damping, external damping, ply angle, length-diameter ratio, stacking sequence, and eccentic distance are numerically analyzed, the effects of above parameters on stable forced vibration-response behaviors of rotating nonlinear composite shaft are discussed. The results show that the internal damping coefficient of angle-ply laminated shaft increases as the increase of ply angle. The primary resonance curves appeared at forward linear natural frequency are found to be of the hardening type. The developed model is capable of describing primary resonance behaviors of rotating composite shaft. This is an important generation of nonlinear dynamic model of in-extensional rotating isotropic shaft.