Optimal Span Lengths for Mitigating Train-Induced Resonance in Seismically Isolated Bridges

This study presents a wavenumber–amplitude spectral envelope approach for optimizing span lengths of seismically isolated railway bridges to mitigate train-induced resonance. The bridge is modeled as an elastically supported beam subjected to moving trainloads, and optimal (cancellation) and critical (resonance) spans are identified directly from the spectral envelope, avoiding computationally intensive extremum-solving of integral response expressions. By replacing complex numerical searches with an envelope-based graphical procedure, the method achieves efficient span identification while remaining adaptable to multi-mode analysis and bearing-stiffness effects. The coupled train-bridge interaction results confirm that optimized spans significantly reduce resonance amplification while meeting design and serviceability requirements. The proposed approach offers a practical, design-oriented tool for the preliminary planning of seismically isolated bridges.