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Bouc hysteresis without an elastic restoring force under white noise excitation using the beta distribution
Author(s) -
Kasess Christian H.,
Waubke Holger
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900300
Subject(s) - restoring force , white noise , excitation , hysteresis , tangent , noise (video) , displacement (psychology) , statistical physics , physics , beta distribution , nonlinear system , mathematical analysis , distribution (mathematics) , work (physics) , mathematics , classical mechanics , computer science , geometry , statistics , psychology , quantum mechanics , artificial intelligence , image (mathematics) , psychotherapist , thermodynamics
The Bouc model comprises three coupled first‐order differential equations which describe the behavior of hysteretic materials. Closure methods have been shown to yield good approximations of the probability density of the state variables under white noise excitation. Previously, a new closure approach for hysteretic softening behavior was introduced, utilizing the beta distribution together with a non‐linear mapping using the inverse hyperbolic tangent. This allows to properly model the finite support of the distribution of the hysteretic force. In the current work, this beta closure approach was applied to single‐degree‐of‐freedom‐systems under stationary white noise excitation lacking, however, an elastic restoring force. Thus, no stationary state is reached. Although the results show a good agreement with Monte‐Carlo simulations there are still deviations in certain higher order moments of the displacement and the velocity depending on the noise strength.