Asynchronous parametric excitation: validation of theoretical results by electronic circuit simulation

Abstract

A validation of recent theoretical results on the stability effects of asynchronous parametric excitation is presented. In particular, the coexistence of both resonance and anti-resonance at each combination resonance frequency is to be confirmed on a close-to-experiment simulation model. The simulation model reproduces the experimental setup developed by Schmieg in 1976, remaining the only experimental study on asynchronous excitation to this day. The model consists of two oscillating electronic circuits with feedback-free coupling through parametric excitation. In contrast to a mechanical system, the phase relations of the parametric excitation terms in an electronic system can be easily adjusted. The implementation of the simulation model is performed in the electronic circuit simulation software LTspice. The electronic model itself is first validated against the experimental results obtained by Schmieg and is then used to confirm the theoretical findings. The results of the electronic circuit simulation show excellent qualitative and quantitative agreement with analytical approximations confirming the coexistence of resonance and anti-resonance effects near a combination resonance frequency.