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The Integration of Nonlinear Stochastic Systems with Applications to the Damage and Ambiguity Identification
Author(s) -
Wedig W.
Publication year - 1981
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.19810610103
Subject(s) - duffing equation , nonlinear system , mathematics , piecewise linear function , gaussian , piecewise , ambiguity , normalization (sociology) , mathematical analysis , statistical physics , computer science , physics , quantum mechanics , sociology , anthropology , programming language
The paper investigates nonlinear stochastic systems with piecewise linear characteristics whose multi‐dimensional distribution densities are piecewise gaussian and therefore exactly calculable taking into account the necessary continuity and normalization conditions. Applying this approach to a cracked bending oscillator a spectral analysis is performed leading to the new phenomenon that the one degree of freedom system possesses two resonances the distance of which is a measure for the damage extension. In case of a vibrator with a piecewise progressive elasticity the spectral analysis is extended to amplitude frequency distributions in order to show the stochastic analogon to the ambiguity of the deterministic Duffing problem.