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Title: Resonance in Preisach systems (English)
Author: Krejčí, Pavel
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 45
Issue: 6
Year: 2000
Pages: 439-468
Summary lang: English
Category: math
Summary: This paper deals with the asymptotic behavior as $t\rightarrow \infty $ of solutions $u$ to the forced Preisach oscillator equation $\ddot{w}(t) + u(t) = \psi (t)$, $w = u + {\mathcal P}[u]$, where $\mathcal P$ is a Preisach hysteresis operator, $\psi \in L^\infty (0,\infty )$ is a given function and $t\ge 0$ is the time variable. We establish an explicit asymptotic relation between the Preisach measure and the function $\psi $ (or, in a more physical terminology, a balance condition between the hysteresis dissipation and the external forcing) which guarantees that every solution remains bounded for all times. Examples show that this condition is qualitatively optimal. Moreover, if the Preisach measure does not identically vanish in any neighbourhood of the origin in the Preisach half-plane and $\lim _{t\rightarrow \infty } \psi (t) = 0$, then every bounded solution also asymptotically vanishes as $t\rightarrow \infty $. (English)
Keyword: Preisach model
Keyword: hysteresis
Keyword: forced oscillations
Keyword: asymptotic behavior
MSC: 34C10
MSC: 34C11
MSC: 34C55
MSC: 34D40
MSC: 47H30
MSC: 82D40
idZBL: Zbl 1010.34038
idMR: MR1800964
DOI: 10.1023/A:1022333500777
Date available: 2009-09-22T18:05:08Z
Last updated: 2020-07-02
Stable URL:
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