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Stability of nonlinear viscoelastic systems under stochastic excitation
Author(s) -
Potapov Vadim
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510104
Subject(s) - nonlinear system , mathematics , viscoelasticity , stability (learning theory) , differential equation , mathematical analysis , stochastic differential equation , gaussian , lyapunov exponent , lyapunov function , plane (geometry) , numerical stability , numerical analysis , physics , computer science , geometry , quantum mechanics , machine learning , thermodynamics
The dynamic behaviour of viscoelastic system with due account of finite deflections but under condition of small strains is described by the system of nonlinear integro‐differential equations. On an example of a thin plate subjected to loads, which are assumed as random wide‐band stationary noises and applied in the plate plane, the stability of nonlinear systems is considered. The stability in a case of finite deflections of the plate is considered as stability with respect to statistical moments of perturbations and almost sure stability. For the solution of the problem, a numerical method is offered, which is based on the statistical simulation of input stochastic stationary processes, which are assumed in the form of Gaussian ”colored” noises, and on the numerical solution of integro‐differential or differential equations. The conclusion about the stability of the considered system is made on the basis of Lyapunov exponents. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)