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<p>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.</p><p></p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月15日

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  • Xinjie Liu,
  • Haiyan Hu,
  • Rumeng Liu,
  • Lifeng Wang

摘要

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.