In this paper, a new equivalent lumped parameter model is proposed for describing the vibration of beams under the moving load effect. Also, an analytical formula for calculating such vibration for low-speed loads is presented. Furthermore, a MATLAB/Simulink model is introduced to give a simple and accurate solution that can be used to design beams subjected to any moving loads, i.e., loads of any magnitude and speed. In general, the proposed Simulink model can be used much easier than the alternative FEM software, which is usually used in designing such beams. The obtained results from the analytical formula and the proposed Simulink model were compared with those obtained from Ansys R19.0, and very good agreement has been shown. It was found that the maximum vibration occurs when the load speed is about 0.58 of the critical speed of the beam. Furthermore, the vibration amplitude resulting from a moving load can amplify to 1.65 times the deflection produced by an equivalent static load.
