Analysis of non-linear stochastic oscillations by the averaging method

Autor:	Zh.B. Bakirov, V.F. Mikhailov
Rok vydání:	2014
Předmět:	Applied Mathematics Mechanical Engineering Multiplicative function Mathematical analysis Fast Fourier transform Markov process Parameter distribution Action (physics) Nonlinear system symbols.namesake Amplitude Mechanics of Materials Modeling and Simulation symbols Mathematics
Zdroj:	Journal of Applied Mathematics and Mechanics. 78:512-517
ISSN:	0021-8928
DOI:	10.1016/j.jappmathmech.2015.03.010
Popis:	The solution of a quasiconservative non-linear oscillatory system is considered, the right-hand sides of which are proportional to a small parameter. Fundamental relations for solving the problem are obtained by changing to “slow” variables and a combination of the stochastic averaging method and the theory of Markov processes. An efficient numerical algorithm is developed based on the fast Fourier transform that enables the output parameter distribution density and the amplitudes of the oscillations to be obtained. Application of the theory to solve the Duffing–van der Pol equation for an additive and multiplicative stochastic action is considered.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8243c7bda81f9e836fdb25e3195403be https://doi.org/10.1016/j.jappmathmech.2015.03.010 Zobrazit plný text záznamu Full Text from ScienceDirect