Mode Coupling in Dynamic Atomic Force Microscopy

Chandrashekar, Abhilash; Belardinelli, Pierpaolo; Lenci, Stefano; Staufer, U.; Alijani, Farbod

doi:10.1103/physrevapplied.15.024013

Cited by 11 publications

(14 citation statements)

References 26 publications

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“…Before proceeding with the sparse identification, elimination of non-candidate functions from the library Θ ( X ) is necessary to improve the interpretability of the predicted models and avoid ill-conditioned matrices or large computational times. 34 In order to achieve this, we augment the optimization problem defined in eqn (2) with constraints derived from experiments, 43 the details of which are provided in the Methods section.…”

Section: Resultsmentioning

confidence: 99%

Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy

et al. 2022

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Section: Resultsmentioning

confidence: 99%

Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy

et al. 2022

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“…Literature presents single-degree-of-freedom reduced-order models using the Galerkin spectral projection [23]. The influence of higher modes of vibration in the nonlinear dynamics of AFM microcantilevers has recently come under scientific scrutiny [24]. As a matter of fact, when aiming to accurately measure the sample mechanical characteristics, additional observables could provide major insights [25].…”

Section: Introductionmentioning

confidence: 99%

Non-Smooth Dynamics of Tapping Mode Atomic Force Microscopy

Belardinelli

Chandrashekar

Alijani

et al. 2022

Volume 9: 18th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC)

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This paper investigates the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include Van der Waals and Derjaguin-Müller-Toporov contact forces. We study the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. The overall dynamical response scenario is evaluated via bifurcation loci maps in the set of parameters of the discontinuous model. We showcase the influence of different dissipation mechanisms activated when the AFM is in contact or out-of contact with the sample. The robustness of the stable solution in the repulsive regime is studied via local and global analyses. The impacting non-smooth dynamics framed within a higher-mode Galerkin discretization is able to capture windows of irregular and complex motion.

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“…Mode coupling is also closely linked to nonlinear dissipation [9,18], and can be tuned utilizing internal resonance (IR); a condition at which two or more resonance frequencies become commensurate. The application of IR in mechanical resonators spans from frequency division [19] and time-keeping [20,21] to enhancing the sensitivity of scanning probe techniques [22].…”

Section: Introductionmentioning

confidence: 99%

Symmetry-breaking induced frequency combs in graphene resonators

Keşkekler¹,

Arjmandi²,

Steeneken³

et al. 2022

Preprint

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Nonlinearities are inherent to the dynamics of two-dimensional materials. Phenomena like intermodal coupling already arise at amplitudes of only a few nanometers, and a range of unexplored effects still awaits to be harnessed. Here, we demonstrate a route for generating mechanical frequency combs in graphene resonators undergoing symmetry-breaking forces. We use electrostatic force to break the membrane's out-of-plane symmetry and tune its resonance frequency towards a two-to-one internal resonance, thus achieving strong coupling between two of its mechanical modes. When increasing the drive level, we observe splitting of the fundamental resonance peak, followed by the emergence of a frequency comb regime. We attribute the observed physics to a non-symmetric restoring potential, and show that the frequency comb regime is mediated by a Neimark bifurcation of the periodic solution. These results demonstrate that mechanical frequency combs and chaotic dynamics in 2D material resonators can emerge near internal resonances due to symmetry-breaking.

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Mode Coupling in Dynamic Atomic Force Microscopy

Cited by 11 publications

References 26 publications

Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy

Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy

Non-Smooth Dynamics of Tapping Mode Atomic Force Microscopy

Symmetry-breaking induced frequency combs in graphene resonators

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