Speaker
Description
Nonlinear interactions in resonant systems play a key role in many physical and engineering phenomena, but experimentally determining their coupling strengths remains challenging, particularly in multimode structures. We introduce a frequency‑domain framework that enables direct experimental quantification of nonlinear modal couplings in multi‑mode nanomechanical resonators using tailored multi‑tone excitation. In our approach, dual‑tone drives placed near selected resonances, combined with additional probing tones at higher‑order modes, generate sideband responses that isolate specific modal interactions. By applying an inverse reconstruction procedure to these sidebands, we extract the corresponding nonlinear coupling strengths and reconstruct fully experimental, device‑specific nonlinear reduced‑order models.
Applied to high‑stress Si₃N₄ nanostrings, the method enables quantification of linear parameters, Duffing nonlinearities, and pairwise coupling coefficients across the first five vibrational modes. The resulting experimentally derived models shows excellent agreement with finite‑element‑based nonlinear models, demonstrating both the accuracy and robustness of the approach.
Because the method relies purely on controlled nonlinear mixing, it does not require operating in internal‑resonance conditions or performing time‑domain ring‑down measurements. The procedure scales naturally to higher‑order interactions and can be extended to systems exhibiting quadratic or hybrid couplings. Overall, this framework provides a general, data‑driven route for characterizing complex nonlinear interactions in micro‑ and nanoscale resonant systems.
A preprint detailing our approach can be found on: https://arxiv.org/html/2604.13920v1