General conditions for the resonance and cancellation of railway bridges under moving train loads

Abstract

The objective of this paper is to elucidate the general conditions of resonance and cancellation for Bernoulli-Euler beam-based bridges subject to moving train loads. Firstly, the bridge's vibration shape is approximated based on the modal superposition method and Fourier series expansion. Then, the semi-analytical solution of the bridge vibrations under moving train loads is derived. After that, the general conditions of train-induced bridge resonance and cancellation are further derived, analyzed, and classified. In particular, cancellation is divided into three classes: case 1, case 2-I, and case 2-II. It is found that the resonance condition for simply-supported bridges is applicable to arbitrary Bernoulli-Euler beam-based bridges, while the cancellation conditions are related to the cancellation classes and modal characteristics of bridges. Finally, three examples are used to validate the semi-analytical solution of bridge vibrations as well as the general conditions of resonance and cancellation, including a simply-supported bridge, a continuous-beam bridge, and a long-span extradosed cable-stayed bridge. Besides, these examples show that for simply-supported bridges, both the resonance and cancellation should be considered, while for bridges with a long-span length or low fundamental frequencies, cancellation is more significant than resonance.