We consider random vibrations of road vehicles excited by random road surfaces. The vehicle is modeled as a multibody system consisting of rigid bodies coupled by springs and dampers. Characteristics of springs and dampers are approximated by polynomials. The resulting mathematical model is a system of nonlinear ordinary differential equations of second order with random input functions. Its solution is found by using perturbation method. Approximations of correlation and spectral density functions of motions, velocities and accelerations of the rigid bodies are calculated using limit theorems of weakly correlated random functions.
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