# Amplitude Stochastic Response of Rayleigh Beams to Randomly Moving Loads

## TL;DR

This paper analyzes the nonlinear stochastic response of Rayleigh beams subjected to randomly moving loads, providing analytical estimates and numerical validation of amplitude behavior under stochastic load velocities.

## Contribution

It introduces an analytical framework combining Fourier transform, residues, and stochastic averaging to study nonlinear beam responses to stochastic moving loads.

## Key findings

- Mean amplitude exhibits nonmonotonic behavior with load velocity variability.
- Analytical results align well with numerical simulations.
- Load number influences the system's response significantly.

## Abstract

We consider the problem of the nonlinear response of a Rayleigh beam to the passage of a train of forces moving with stochastic velocity. The Fourier transform and the theory of residues is used to estimate the mean-square amplitude of the beam, while the stochastic averaging method gives the stationary probability density function of the oscillations amplitude. The analysis shows that the effect of the load random velocities is highly nonlinear, leading to a nonmonotonic behavior of the mean amplitude versus the intensity of the stochastic term and of the load weight. The analytic approach is also checked with numerical simulations. The effect of loads number on the system response is numerically investigated.