Transverse forced vibration of axially moving Timoshenko beam at a supercritical speed
TAN Xia1, DING Hu1, Chen Li-qun1,2
1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072;
2. Department of Mechanics, Shanghai University, Shanghai 2004444
In this paper, the transverse nonlinear forced vibration of axially moving Timoshenko beam at a supercritical speed is studied under external excitation. In the supercritical region, the standard control equation of gyro system, which under the lateral external incentives, is derived based on the governing equation of transverse nonlinear vibration of axially moving Timoshenko beam. Moreover, the steady-state amplitude frequency response relationship of axially moving Timoshenko beam at a supercritical speed is researched by using Galerkin method. Furthermore, the effects of system parameters on the steady-state amplitude frequency response relationship of Timoshenko beam are considered. Besides, comparisons with Euler-Bernoulli (E-B) beam reveal that the resonance frequency of Timoshenko beam is much lower and the resonance amplitude is higher in the supercritical region.
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