Vibration of a Simple Beam Subjected to a Moving Sprung Mass with Initial Velocity and Constant Acceleration

In this paper, a semi-analytical solution to the problem of a simply supported beam subjected to a moving sprung mass with initial velocity and constant acceleration or deceleration was presented, which serves as a benchmark for checking the performance of other numerical methods. Herein, a finite element modeling procedure was adopted to tackle the vehicle–bridge interaction, and the responses of the vehicle and bridge were computed by time integration schemes such as the Newmark average acceleration, HHT-[Formula: see text], and Wilson-[Formula: see text] methods. In comparison with the semi-analytical solution, the acceleration response of the beam solved by the Newmark average acceleration method shows spurious high-frequency oscillations caused by the finite element discretization. In contrast, the HHT-[Formula: see text] and Wilson-[Formula: see text] methods can dissipate these oscillations and show more accurate results. Moreover, we found that the dynamic responses of the beam and sprung mass were mainly determined by the initial velocity of the sprung mass, but not by the acceleration or deceleration.