Train-speed sensitivity approach for maximum response envelopes in dynamics of railway bridges

The design of high-speed railway bridges is strongly conditioned by vibrations and resonance amplifications induced by rail traffic. Furthermore, most current dynamic analysis approaches are computationally expensive, what poses an obstacle to the study of structural alternatives at early design stages. In order to address this limitation, this paper presents a semi-analytic meta-model based on train speed sensitivity analysis. This technique exploits the sensitivity of the dynamic response of bridges to train speed variations or, in other words, the slopes of the maximum response envelopes. The only approximation of this technique stems from the spatial discretization by finite element modelling and modal superposition, while the formulation is closed-form in the time domain. In this way, it is possible to efficiently compute envelope values and sensitivities with moderate train speed sampling frequencies and, afterwards, approximate the remaining speeds through a cubic spline interpolation. Four case studies are presented in order to illustrate the potentials of the proposed technique, including from simply supported beams to complex three-dimensional models. The numerical results report substantial reductions in the computation time and storage requirements, proving the present approach to be a valuable tool for rapidly assessing the performance of design alternatives.