Nonlinear dynamic modeling and response analysis of a rotor-blade system with whirling motion

Abstract

In this paper, we propose a new nonlinear dynamic model of a rotor-blade system with whirling motion, in which a rigid rotor and blades are modeled as a Jeffcott rotor and Euler-Bernoulli beams, respectively. The stiffening effects of the rotating blades are considered using a hybrid set of deformations, which consist of the stretch and chordwise deformations. After the nonlinear partial differential equations of motion are derived using Hamilton's principle, they are discretized using the Galerkin method. From the discretized equations, the nonlinear dynamic responses are computed using the generalized-alpha time integration method. Based on the dynamic responses and the frequency spectra, the proposed model is verified both for the case where the blade is considered to be a rigid body and for the case where there is no whirling motion of the rotor. In this study, the nonlinear dynamic responses of the rotor-blade system are analyzed in terms of the natural frequencies for whirling motion and the natural frequencies of the deformation of the rotating beam. In addition, the effects of the supporting stiffness, rotating speed and blade stiffness on the dynamic responses of the radial displacement and stretch/chordwise deformations are also analyzed.