Closed-form solutions for non-stationary responses of Euler beams with general boundary conditions under fully coherent stochastic wheel-rail forces

• Published in: Probabilistic engineering mechanics Vol. 81; p. 103796
• Main Authors: Wang, Bin, Yu, Helu, Wang, Zewen, Wang, Huiding, Li, Yongle
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2025
• Subjects: Closed-form solution; Euler beam; General boundary condition; Random vibration analysis; Stochastic wheel-rail forces; Track irregularity; Track irregularity; Closed-form solution; Random vibration analysis; Stochastic wheel-rail forces; Euler beam; General boundary condition
• ISSN: 0266-8920
• DOI: 10.1016/j.probengmech.2025.103796

The random vibration analysis of beams subjected to train loads is an interesting research subject in the field of civil engineering. Two critical problems in this subject deserving further study are how to reasonably model the random wheel-rail forces and efficiently evaluate the response statistics of beams. This paper aims to contribute to addressing these two problems. First, an appropriate wheel-rail force model that can accurately represent the statistical characteristics of train loads is established, where the wheel-rail forces are modelled as a series of stationary stochastic processes with fixed time delays, and their inherent relation with the track irregularity is established based on the frequency-domain random vibration theory. Next, an approach combining the spectral decomposition and modal superposition techniques is proposed to derive a closed-form response expression for the Euler beams with general boundary conditions, which can be further used to accurately and efficiently evaluate the time-frequency response statistics of beams. In the numerical examples, the evolutionary spectral method and Monte Carlo simulation are used to demonstrate the performance of the proposed method, and the effects of several parameters of the wheel-rail force model on the stochastic responses of the beams are investigated. •A wheel-rail force model capable of accurately representing statistical characteristics of train loads;•Closed-form solutions derived for responses of Euler beams with general boundary conditions;•Random vibration approach combining spectral decomposition and modal superposition techniques;•Effect of parameters and speed of wheel-rail forces on stochastic responses of beams are investigated.