Path-dependent dynamic response in nano graphite membrane resonators under elastic boundary modulation

Boundaries govern how a system moves or deforms, yet their own dynamics have long been treated as negligible. In a two-dimensional (2D) material resonator, where the van der Waals interfaces replace conventional hinged and clamped boundaries, subtle interfacial motions can reorganize strain and energy, governing the nonlinear behavior of the resonator. In this work, we reveal that the nano graphite membrane resonators with elastic boundaries exhibit path-dependent nonlinear dynamics, in which the resonance behavior depends not only on the driving amplitude but also on the direction and speed of the frequency sweep. This elasticity produces bifurcation behaviors and frequency shifts during frequency sweeps. Higher-order modes further exhibit geometry-dependent nonlinearities determined by the alignment between the modal strain and boundary orientation. These results identify dynamic boundary elasticity as hidden degrees of freedom for the nonlinear responses in 2D resonators and provide a platform for probing interfacial friction at the nano-scale. Mechanical boundaries strongly influence the vibration of two-dimensional resonators, yet their own dynamics is often over looked. Here, the authors demonstrate that tuning the graphite–substrate contact area produces recoverable elastic boundaries, which give rise to resonance shifts and bifurcation behavior governed by the sweep direction and sweep rate.