Extended harmonic input method for response spectrum determination of vehicle-bridge systems

The calculation of response power spectral densities (PSDs) from the excitation PSDs of vehicle-bridge (VB) systems is crucial for the safety evaluation of operating vehicles, bridge fatigue analysis, and vibration control optimization. However, calculations using the available methods result in considerable computational errors when applied to evaluate the response PSDs of VB systems. Hence, an extended harmonic input method (HIM) is proposed to compute the time-varying response spectrum in VB systems. First, the unique characteristics of VB systems that may cause the inapplicability of conventional methods are systematically analyzed. Subsequently, an extended version of the HIM is mathematically established to calculate the time-varying response spectrum of VB systems via the representation of inputs and decomposition of responses. Finally, a numerical example of an actual high-speed railway bridge subjected to track irregularities or seismic excitations is presented to illustrate the efficacy of the novel method.