Stability of linear parametric oscillator with dissipation
Anton V. Bolovin
ISIC “WESTA”, Dnipropetrovsk, Ukraine
The paper is received on December 7, 2014
Abstract. Influence of dissipation
on the parametric excitation of a linear system is considered in the framework
of the Meissner model. Equation transition curves and attenuation threshold
were obtained for parametric oscillations in a linear oscillator. Developed in
this paper an approach is directly applicable to the corresponding problem in
the theory of wave propagation in spatially modulated structures.
Key words: parametric resonance,
model Meissner, translation matrix, Floquet theorem, stability of solutions,
transition curves, threshold attenuation.