An Approach to Quantifying the Distribution of Resonance and Cancellation Train Speeds of Railway Bridges with Random Uncertainties

Resonance and cancellation phenomena are fundamental scientific topics in the field of train-bridge interactions. Prior studies have explained their underlying mechanisms and consequential effects. This paper re-examined the two phenomena from a random perspective and delineated them as random resonance and random cancellation. Subsequently, a practical framework is proposed to quantify the probability distributions of train speeds that induce the resonance and cancellation in railway bridges considering random uncertainties. The proposed framework incorporates the input parameter design, stochastic modal analysis, modal identification, and sparse polynomial chaos expansion (PCE). In the modal identification, a novel indicator was developed which aids in identifying modal shapes and constructing eigenpairs involving eigenvalues and modal shapes. The framework's validity and efficiency were confirmed using three bridge examples: a simply supported bridge, a continuous beam bridge, and a long-span cable-stayed bridge. The results show that the critical speeds for the resonance and cancellation exhibit significant variabilities. This work is expected to provide some reference for determining reasonable train operation speeds and optimizing railway bridge design.