Dynamic response of arch bridges traversed by high-speed trains

A mechanical model describing the planar elasto-dynamics of arch bridges with general arch profiles is presented. The model is amenable to analytical or semi-analytical treatments and is effective for parametric studies, design of control systems or structural optimizations. The Ritz's energy approach is employed to calculate the solutions of the vibration eigenvalue problem—natural frequencies and mode shapes—and the forced responses to external excitations, namely those induced by the passage of trains. A closed-form solution of the bridge dynamic response to the transit of trains with arbitrary load distributions and running speeds is found and the train-induced resonances are accordingly discussed. In particular, three European high-speed trains—the French TGV, the Italian ETR 500, and the German ICE—traversing a lower-deck steel arch bridge are considered and the ensuing responses are investigated.