Dynamic Response of Slope Inertia-Based Timoshenko Beam under a Moving Load
Tuo Lei; Yifei Zheng; Renjun Yu; Yukang Yan; Ben Xu
In this paper, the dynamic response of a simply supported beam subjected to a moving load is reinvestigated. Based on a new beam theory, slope inertia-based Timoshenko (SIBT), the governing equations of motion of the beam are derived. An analytical solution is presented by using a coupled Fourier and Laplace&ndash:Carson integral transformation method. The finite element solution is also developed and compared with the analytical solution. Then, a comparative study of three beam models based on the SIBT, Euler&ndash:Bernoulli and Timoshenko, subjected to a moving load, is presented. The results show that for slender beams, the dynamic responses calculated by the three theories have marginal differences. However, as the ratio of the cross-sectional size to beam length increases, the dynamic magnification factors for the mid-span displacement obtained by the SIBT and Timoshenko beams become larger than those obtained by the Euler&ndash:Bernoulli beams. Furthermore, until the ratio is greater than 1/3, the difference between the calculated results of the SIBT and Timoshenko beams becomes apparent.
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