  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.
