Parametric Instability in Mathieu Equation for Interaction P-S Waves

Abstract

We propose an experimental study of parametric resonance between P-waves and S-waves, which can be used to describe various nonlinear phenomena qualitatively and to obtain bifurcation diagrams quantitatively. It is based on an electronic circuit and is easy to design. We show that it is a good simulation of parametric phenomena, and our results are in good agreement with theoretical predictions. In particular, it may be used to study the influence of pump P waves on the instability’s threshold and amplitude of S waves.