Observation of three-mode parametric instability in a micromechanical resonator

We present systematic experimental observations of three-mode auto-parametric instability in a micromechanical resonator analogous to previous experimental observations of this effect in optical parametric resonators. The three-mode instability is triggered when a driven mode at frequency ωd couples to two lower frequency modes (frequencies ω1 and ω2) such that ωd = ω1 + ω2. Similar to the 2 mode instability, the phenomenon is seen to be threshold dependent and sensitive to driving conditions and system parameters. In support of the experimental observations, a dynamical model has also been specified.