Vibrations Analysis of Multi-Span Beams Under a Moving Force Using SEM

초록

A structure subjected to moving loads may experience severe vibrations to cause structural failures. Thus, it is important to predict vibration characteristics of such structures accurately. FEM is known as a powerful solution technique to deal with most complex structural dynamics problems. However, in general, it requires very fine meshes to improve solution accuracy. Thus, as an alternative to FEM, a spectral element method (SEM) is developed in this study for the vibration analysis of a multi-span beam subjected to a moving point force. The basic concept used in this study was originally developed in an author’s previous study for single-span beams subjected to a stationary point force. In this study, each span of a multi-span beam is represented by the Timoshenko beam model. The moving point force given in the time domain is transformed to the frequency domain using DFT as a series of quasi-static stationary point forces acting on the beam simultaneously. The dynamic responses are then obtained by superposing all individual dynamic responses excited by each quasi-static point force. As the SEM based on the original one-element method (OEM) gives exact individual dynamic responses for all spans except for the span at which the quasi-static point force is located, the exact dynamic responses for this span are obtained based on the modified OEM by simply adding some correction terms, which are given in the closed analytical forms.