Excitation of multiple 2-mode parametric resonances by a single driven mode

TL;DR

This paper demonstrates that a single driven mechanical mode can excite multiple sub-harmonic modes through autoparametric resonance, revealing a threshold-dependent process influenced by parametric back-action, with implications for multi-mode mechanical systems.

Contribution

It introduces a general physical framework and modified dynamical equations for understanding multi-mode autoparametric excitation by a single primary mode.

Findings

Multiple sub-harmonic modes can be excited by one primary mode within its bandwidth.

The excitation process is threshold-dependent and exhibits parametric back-action.

Experimental results support the proposed theoretical model.

Abstract

We demonstrate autoparametric excitation of two distinct sub-harmonic mechanical modes by the same driven mechanical mode corresponding to different drive frequencies within its resonance dispersion band. This experimental observation is used to motivate a more general physical picture wherein multiple mechanical modes could be excited by the same driven primary mode within the same device as long as the frequency spacing between the sub-harmonic modes is less than half the dispersion bandwidth of the driven primary mode. The excitation of both modes is seen to be threshold-dependent and a parametric back-action is observed impacting on the response of the driven primary mode. Motivated by this experimental observation, modified dynamical equations specifying 2-mode auto-parametric excitation for such systems are presented.