Dynamic Analysis of Linear and Nonlinear Oscillations of a Beam Under Axial and Transversal Random Poisson Pulses

This paper proposes an approximate explicit probability density function for the analysis of external and parametric oscillation of a simply supported beam driven by random pulses. The impulsive loading model adopted is Poisson white noise, which is a process having Dirac delta occurrences with random intensity distributed in time according to Poisson's law. The response probability density function can be obtained by solving the related Kolmogorov–Feller integro-differential equation. An approximate solution is derived by transforming this equation to a first-order partial differential equation. The method of characteristics is then applied to obtain an explicit solution. The theory has been validated through numerical simulations.