Finite element and numerical vibration analysis of a Timoshenko and Euler–Bernoulli beams traversed by a moving high-speed train

Abstract

In this paper, two different numerical methods are presented for the dynamic response of Euler–Bernoulli and Timoshenko beam under the impact of 10-DOF high-speed train (HST). Bridge beam is modeled in simply supported and uniform structure. The train traveling at high and constant speed on the bridge is modeled by taking into consideration primary and secondary suspension systems. The motion equation of the system was obtained using the Hamilton principle. These differential equations have been solved in the time domain using the fourth-order Runge–Kutta algorithm. The motion equations of the system have been converted to finite element format using Galerkin’s weak-form formulation. The finite element solution of the system was solved using the Newmark-β algorithm, and both algorithms were compared. In addition, Timoshenko beam theory and Euler–Bernoulli beam theory presented in the study were compared in terms of both bridge dynamics and train dynamics. As a result, although the speed difference between the two theories is significant at the critical speed values of HST, this difference in certain speed values decreases considerably.