Spectral and cross-spectral densities expressions’ refinement for rail vehicle oscillations

Abstract

In this paper, we derive analytical expressions describing spectral and mutual spectral densities of random processes by performing analytical Fourier transform of the corresponding correlation functions. On the basis of accepted analytical expressions for correlation functions of differentiable random processes, analytical expressions for spectral density and mutual spectral density components, which is a complex frequency function, are derived. The influence of the accepted analytical expressions on the correlation functions, spectral densities, and mutual spectral density components (real, imaginary, amplitude, and phase) on the parameters is presented. Plots obtained using obtained analytical expressions have showed full convergence with those obtained by direct integration of the analytical expression of the correlation function. The analytical expressions given in this paper may be used for investigating various random processes. In particular, spectral and reciprocal spectral densities can be used for approximation of experimentally received spectral densities, including equivalent geometrical irregularities of a rail track and random fluctuations of a rail vehicle. The parameters of analytical expression obtained by such an approximation can be used for generation of analogous experimental multidimensional random processes in the tasks of mathematical modelling.