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Non-stationary random vibration analysis of a three-dimensional train-bridge system using spectral decomposition-based explicit time-domain method
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DOI：10.1016/j.compstruc.2025.108091.png)
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Abstract
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By introducing the spectral decomposition-based explicit time-domain method, this paper presents an innovative computational framework for analyzing the non-stationary random vibration problem in a three-dimensional train-bridge system involving multi-variate random track irregularities. First, the time-dependent train-bridge model is formulated by coupling the train and bridge dynamics via a spatial wheel-rail interaction model. Next, the random track irregularities are decomposed through the spectral representation technique, enabling their time-domain discrete characterization in terms of three orthogonal random vectors. Then, an explicit mapping between the system responses and the orthogonal random vectors is constructed by integrating the precise integration method with a finite difference approach, leading to a recursive formulation that facilitates efficient computation of the response coefficient matrices. The obtained explicit response formulation allows straightforward computation of time–frequency response statistics of the train-bridge system, eliminating the need for repetitive time-domain simulations or extensive numerical integrations commonly associated with conventional non-stationary random vibration techniques. Lastly, the pseudo-excitation method and Monte Carlo simulation are adopted to verify the applicability of the proposed method, a comprehensive parametric investigation is also conducted to examine the individual contributions from different track irregularity components on the stochastic dynamic behavior of the train-bridge system.
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