Vibration of a beam subjected to a moving force: Frequency-domain spectral element modeling and analysis

A frequency domain spectral element method (SEM) is proposed for the vibration analysis of a beam subjected to a moving point force. In the proposed method, Timoshenko beam theory is applied to the beam and the entire span of the beam is represented by a two-element model. The moving point force is assumed to be a point force of constant magnitude moving at a constant speed or a time-varying speed. The discrete Fourier transformed moving point force is expressed as a function of spatial coordinate (x). Therefore, the moving point force can be considered in the frequency domain as the superposition of a series of stationary point forces. Accordingly, the total vibration response due to a moving point force can be obtained by superposing individual vibration responses due to each stationary point force. The performance of the proposed two-element method-based SEM is numerically evaluated by comparison with solutions from an existing modal analysis method and the standard finite element method.