Enhanced nonlinear damping in graphene by parametric-direct internal resonance

Nonlinearities are ubiquitous in nanomechanical systems. They manifest themselves already at low vibration amplitudes, alter the stiffness and unlock energy decay paths through intermodal couplings. Although strong nonlinear stiffness variations have been observed in nanomechanical systems, to date, their nonlinear damping is conceived to be a fixed parameter, independent from the drive level or frequency. In this letter, we experimentally show that nonlinear damping of graphene nanodrum resonators can be strongly enhanced via parametric-direct internal resonance. By regulating the drive level, we tune the parametric resonance of the nanodrum over a large range of 40-70 MHz to reach two-to-one internal resonance, while demonstrating a nearly two-fold increase of the nonlinear damping. We derive an analytical model that captures the observed physics, and provides supporting evidence that nonlinear damping is amplified near internal resonance. Our study opens up an exciting route towards utilizing modal interactions and parametric resonance at nanoscale for realizing resonators with tunable nonlinear damping over wide frequency ranges.