Resonance in Preisach systems
- Krejčí, Pavel
2010 Mathematics Subject Classification
- 34D40 47H30
- Preisach model, hysteresis, forced oscillations, asymptotic behavior
This paper deals with the asymptotic behavior as t → ∞ of solutions u to the forced Preisach oscillator equation ẅ(t) + u(t) = ψ(t), w = u + 𝒫[u], where 𝒫 is a Preisach hysteresis operator, ψ ∈ L∞(0,∞) is a given function and t ≥ 0 is the time variable. We establish an explicit asymptotic relation between the Preisach measure and the function ψ (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 neighborhood of the origin in the Preisach half-plane and limt→∞ψ(t) = 0, then every bounded solution also asymptotically vanishes as t → ∞.
- Appl. Math. 45 (2000), No. 6, pp. 439--468