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

Figure 15

Comparisons of the distributed force, Fourier series coefficients, and central displacements of the fourth span of the purlin between the two high-speed trains (u stands for the central displacement of the purlin under the distributed force due to the head of the train and stands for the central displacement of the purlin under the first sine wave decomposed from the distributed force due to the head of the train).