# Resonance in Preisach systems

Applications of Mathematics (2000)

- Volume: 45, Issue: 6, page 439-468
- ISSN: 0862-7940

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topKrejčí, Pavel. "Resonance in Preisach systems." Applications of Mathematics 45.6 (2000): 439-468. <http://eudml.org/doc/33071>.

@article{Krejčí2000,

abstract = {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 $.},

author = {Krejčí, Pavel},

journal = {Applications of Mathematics},

keywords = {Preisach model; hysteresis; forced oscillations; asymptotic behavior; Preisach model; hysteresis; forced oscillations; asymptotic behavior},

language = {eng},

number = {6},

pages = {439-468},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Resonance in Preisach systems},

url = {http://eudml.org/doc/33071},

volume = {45},

year = {2000},

}

TY - JOUR

AU - Krejčí, Pavel

TI - Resonance in Preisach systems

JO - Applications of Mathematics

PY - 2000

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 45

IS - 6

SP - 439

EP - 468

AB - 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 $.

LA - eng

KW - Preisach model; hysteresis; forced oscillations; asymptotic behavior; Preisach model; hysteresis; forced oscillations; asymptotic behavior

UR - http://eudml.org/doc/33071

ER -

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