Abstract Stationary response of a travelling system to profile-imposed excitation is investigated. The system is treated as linear and both the profile and traversal velocity of the system are considered to be stationary and Gaussian random functions of horizontal distance. The problem is formulated by means of a differential equation with random coefficients, and detailed analysis of vertical vibrations of the system travelling with small random velocity fluctuations is performed. An analytical expression for response spectral density is obtained in a relatively simple form for a general case, and this is used in calculation of the effect of randomly-varying velocity on a system's response in particular cases relevant to vehicle dynamics.
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