Computation of the solutions of the Fokker–Planck equation for one and two DOF systems

Uncertainty in structures may come from unknowns in the modelisation and in the properties of the materials, from variability with time, external noise, etc. This leads to uncertainty in the dynamic response. Moreover, the consequences are issues in safety, reliability, efficiency, etc. of the structure. So an issue is the gain of information on the response of the system taking into account the uncertainties [Mace BR, Worden K, Manson G. Uncertainty in structural dynamics. J Sound Vib 2005;288(3):423–9]. forcing or the uncertainty can be modelled through a white noise, the Fokker–Planck (or Kolmogorov forward) equation exists. It is a partial differential linear equation with unknown p(X, t), where p(X, t) is the probability density function of the state X at time t. s article, we solve this equation using the finite differences method, for one and two DOF systems. The numerical solutions obtained are proved to be nearly correct.