The paper makes a sketch of an SDOF system response analysis subjected to a random excitation having a form of the additive Poisson driven independent random impulses. A special generalised Fokker-Planck equation having a form of an integro-differential equation is presented together with boundary and initial conditions. Later the Galerkin-Petrov process as a method of a numerical solution of the respective evolutionary integro-differential equation for the probability density function (PDF) is presented in general. Various analytic and semi-analytic solution methods have been developed for various systems to obtain results requested. However numerical approaches offer a powerful altemative. In particular the Finite Element Method (FEM) seems to be very effective. Shape and weighting functions for purposes of a numerical solution procedure are carred out and corresponding ordinary differential system for PDF values in nodes is deduced. As a demonstration particular SDOF systems are investigated. Resulting PDFs are analysed and mutually compared. and Obsahuje seznam literatury
The Fokker-Planck (FP) equation is frequently used when the response of the dynamic system subjected to additive and/or multiplicative ramdom noises is investiagted. It provides the probability density function (PDF) representing the key information for further study of the dynamic system. Various analytic and semi-analytic solution methods have been developed for various systems to obtain results requested. However numerical approaches offer a powerful alternative. In particular the Finite Element Method (FEM) seems to be very effective. A couple of single dynamic linear/non-linear systems under additive and multiplicative random excitations are discussed using FEM as a solution tool of the FP equation. and Obsahuje seznam literatury