Random fluctuation of internal forces in rough beams under moving oscillators

A method for evaluating the second-order statistics of internal forces along a rough beam crossed by a linear oscillator is presented. The surface roughness is modeled as a zero-mean Gaussian random field of given Power Spectral Density (PSD). The equations of motion of moving oscillator and supporting beam separately taken are coupled by imposing equilibrium and compatibility conditions at the contact point, properly including the effects of the random surface roughness. Then, in the context of the Conventional Series Expansion (CSE), a set of ordinary differential equations, with time-dependent coefficients, is derived for the second-order statistics of the oscillator-beam response, and an efficient strategy of solution is presented. In order to improve the accuracy of Bending Moment (BM) and Shear Force (SF) statistics, a Quasi-Static (QS) correction term consistent with the Mode Acceleration Method (MAM) is added to the CSE. Numerical results demonstrate the accuracy of the proposed approach through appropriate comparisons with Monte Carlo simulations.