Random vibration of linear oscillators moving on rough beams

An efficient procedure for evaluating the second-order statistics of the response of the coupled dynamic system composed of a linear oscillator moving on a rough beam is presented. The surface roughness is modeled as a spatial zero-mean Gaussian stationary random process. In a first stage, the moving oscillator and the beam are handled as two non-interacting dynamic sub-systems, whose equations of motion are coupled by imposing the equilibrium and the compatibility conditions at the instantaneous position of the moving oscillator, properly accounting for the effects of the random surface roughness. Finally, the ordinary differential equations, with time-dependent coefficients, governing the second-order statistics of the response are derived, and an efficient step-by-step solution procedure is proposed. Numerical results demonstrate the accuracy and the computational efficiency of the presented approach through appropriate comparisons with Monte Carlo simulation data.