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Oscillatory Stochastic Systems with Nonlinear Dissipations
Author(s) -
Wedig V. Walter.,
Wagner Utz Von.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20000801426
Subject(s) - nonlinear system , monte carlo method , dissipation , piecewise , statistical physics , probability density function , stationary distribution , white noise , physics , mathematics , noise (video) , mathematical analysis , computer science , quantum mechanics , statistics , artificial intelligence , markov chain , image (mathematics)
As an example for oscillators with nonlinear dissipation, we consider a piecewise linear and asymmetric damping characteristic which is typical for shock absorbers in wheel suspensions. For white noise excitations, associated Fokker‐Planck solutions are approximated assuming that displacements and velocities of oscillators are independent. To get even better approximations, analytical results of the expected values of the system are taken into consideration. Then, these stationary density approximations are applied to derive adapted orthogonal polynomials by which the stationary probability density is expanded. The analytical results obtained are checked by corresponding Monte‐Carlo simulations.