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.
Highlights
Parametric excitation in mechanical systems is well known for its destabilizing resonance effect and, in recent decades, increasingly for its stabilizing effect, i.e., parametric anti-resonance
The destabilizing effects are widely used in energy harvesting applications [2,27] as well as in parametric amplifiers [12]; on the other hand, the anti-resonance effect is introduced in order to attenuate vibrations and to enhance dissipative properties [11]
While the very complex symbolic expression for Lyapunov characteristic exponents (LCEs) was derived by Schmieg in general form allowing the study of both stabilizing and destabilizing effects of parametric excitation, the analysis was limited to the destabilizing effect only, as the anti-resonance effect was not yet known at that time
Summary
Parametric excitation in mechanical systems is well known for its destabilizing resonance effect and, in recent decades, increasingly for its stabilizing effect, i.e., parametric anti-resonance. Asynchronous parametric excitation: validation of theoretical results terms is rather inadequate for this purpose—the interaction and superposition of different effects make it impossible to study the implications of individual system parameters. For this reason, the validation of the newly discovered stability effects is performed using a close-to-experiment simulation setup of an electronic system based on the real experiment conducted by Schmieg [25]. The electronic simulation model itself is first validated by means of the existing experimental data Based on this validated model, the theoretical findings concerning the coexistence of resonance and anti-resonance are to be confirmed.
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