Fourier Series Approach for the Vibration of Euler–Bernoulli Beam under Moving Distributed Force: Application to Train Gust

Abstract

The dynamic response of an Euler–Bernoulli beam under moving distributed force is studied. By decomposing the distributed force into Fourier series and extending them to semi-infinite sine waves, the complex procedure for solving this problem is simplified to three base models, which are calculated by the modal superposition method further. The method is proved to be highly accurate and computational efficient by comparing with the finite element method. For verifying the theory and exploring the relationship between dynamic pressure due to train gust and vibration of the structure, a site test was conducted on a platform canopy located on the Beijing-Shanghai high-speed railway in China. The results show the theory can be used to evaluate the dynamic response of the beam structure along the trackside due to the train gust. The dynamic behavior of a 4-span continuous steel purlin is studied when the structure is subjected to the moving pressure due to different high-speed train passing.