a b s t r a c tIn this paper, the vibration and stability of an axially moving beam is investigated. The finite element method with variable-domain elements is used to derive the equations of motion of an axially moving beam based on Rayleigh beam theory. Two kinds of axial motions including constant-speed extension deployment and back-and-forth periodical motion are considered. The vibration and stability of beams with these motions are investigated. For vibration analysis, direct time numerical integration, based on a Runge-Kutta algorithm, is used. For stability analysis of a beam with constant-speed axial extension deployment, eigenvalues of equations of motion are obtained to determine its stability, while Floquet theory is employed to investigate the stability of the beam with back-andforth periodical axial motion. The effects of oscillation amplitude and frequency of periodical axial movement on the stability of the beam are discussed from the stability chart. Time histories are established to confirm the results from Floquet theory.
The fatigue damage and fatigue life of a batch of [ 45 °h. graphite/epoxy composite laminates are investigated in the present study. Residual stiffness is selected as a parameter to describe the degradation behavior of the composite laminates. In order to predict the fatigue life and residual stiffness of such laminates, a simple model which contains a residual stiffness degradation equation and the randomization of its parameters is proposed. A Markov chain model is also employed. Both models can be used to predict the probability distribution of the degraded stiffness at a specified loading cycle. The probability distribution of loading cycles for the residual stiffness to degrade to a certain amount can be predicted as well. Experimental data verify the applicability of both models to the studied composite laminates. According to the data, a simple relation between the ultimate strength and fatigue life of the laminates is also found. The relation provides us with quick estimation of the fatigue life of a component based on its ultimate strength which can usually be obtained very easily.
An analytical study of the dynamic characteristics of a geared rotor-bearing system by the transfer matrix method is presented. Rotating shafts of the system are modeled as Timoshenko beams with effects of shear deformation and gyroscopic moment taken into account. The gear mesh is modeled as a pair of rigid disks connected by a spring-damper set along the pressure line and the transmission error is simulated by a displacement excitation at the mesh. The transfer matrix of a gear mesh is developed. The coupled lateral-torsional vibration of a geared rotor-bearing system is studied. Natural frequencies and corresponding mode shapes, and whirl frequencies under different spin speeds are determined. In addition, steady-state responses due to the excitation of mass unbalance, geometric eccentricity and transmission error of gear mesh are obtained. Effect of the time-varying stiffness of the gear mesh is investigated.
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