Electron. J. Diff. Eqns., Vol. 2000(2000), No. 74, pp. 115.
Behavior of forced asymmetric oscillators at resonance
C. Fabry
Abstract:
This article collects recent results concerning the behavior at
resonance of forced oscillators driven by an
asymmetric restoring force, with or without damping. This synthesis
emphasizes the key role played by a function denoted by
,
which is, up to a sign reversal of its argument,
a correlation product of the forcing term
and of a function
representing a free oscillation for theundamped equation.
The theoretical results are accompanied by graphical representations
illustrating the behavior of the damped and undamped oscillators.
In particular, the damped oscillator is considered, with a forcing
term whose frequency is close to the frequency of the free oscillations.
For that problem, frequencyresponse curves are studied, both
theoretically and through numerical computations, revealing a
hysteresis phenomenon, when
is of constant sign.
Submitted September 29, 2000. Published December 14, 2000.
Math Subject Classifications: 34C15, 34C25, 70K30.
Key Words: Resonance, frequencyresponse curves, jumping nonlinearity,
Fucik spectrum.
Show me the
PDF file (467K),
TEX file, and other files for this article.

Christian Fabry
Universite Catholique de Louvain
Institut de Mathematique Pure et Appliquee,
Chemin du Cyclotron, 2 , B1348 LouvainlaNeuve, Belgium
email: fabry@math.ucl.ac.be

Return to the EJDE web page