Dynamic analysis of a multi-span beam subjected to a moving force using the frequency domain spectral element method

This study extends a frequency domain modified spectral element method (SEM) from single-span beams to multi-span beams subjected to moving point forces. Each span is represented by the Timoshenko beam model. The time history of the moving point force is transformed to the frequency domain as a series of quasi-static or stationary point forces acting on the beam simultaneously. The dynamic responses are obtained by superposing the individual dynamic responses excited by each quasi-static point force. The SEM based on the original one-element method provides the exact individual dynamic responses of all spans except for the span on which the quasi-static point force is located. Thus, the exact dynamic responses for this span are obtained based on the modified one-element method by adding some correction terms that are given in closed analytical forms. The method is highly accurate and computationally efficient, as verified by comparison with other techniques such as exact theory, modal analysis method, and finite element method.