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.