Modeling and nonlinear dynamics analysis of a rotating beam with dry friction support boundary conditions

Abstract

A nonlinear dynamic model of a rotating beam with dry friction support boundary conditions is developed, and the effectiveness of this model is verified by comparing it with the relevant literature. In the proposed model, a macro-slip friction model of the contact interfaces at the root of the beam with a dovetail tenon is established to characterize the friction on the beam. Furthermore, a time-domain solution and a linearization method of nonlinear friction force are proposed. The dynamic differential equations of the rotating beam are obtained conveniently by means of Chebyshev polynomials theory. Based on the developed model, the effect of the harmonic number on calculations is discussed by incremental harmonic balance method (IHBM). Moreover, the influences of friction coefficient, excitation amplitude, and rotational speed on the amplitude-frequency response of the system are analyzed. The results indicate that the higher-order harmonic components have significant influence on the nonlinear dynamic response of the tenon-mortise connected beam, which must be considered in the frequency-domain computation. When the contact interface slips, the contact stiffness decreases and the contact damping increases. With the rise of friction coefficient, rotational speed or the decreases of excitation amplitude, the range of slip zone narrows. The variation of amplitude-frequency curves is well explained from the perspective of contact stiffness and contact damping.