Cantilever dynamics in higher-harmonic atomic force microscopy for enhanced material characterization

Potekin, Randi; Dharmasena, Sajith; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.; Cho, Han Na

doi:10.1016/j.ijsolstr.2016.11.013

Cited by 19 publications

(15 citation statements)

References 19 publications

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“…An improvement of the frequency stabilization was reported as driving the arch resonator in the internal resonance regime as shown previously by Antoine et al [31]. Internal resonance was also observed and exploited in carefully designed structures to get commensurate ratios between different modes such as the H-shapes structures [161] and the microcantilevers with outer and inner paddles [162,163]. As conferred in this section, mode coupling among different modes of vibrations has been investigated deeply in the literature using M/NEMS resonators.…”

Section: Internal Resonancementioning

confidence: 56%

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Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

115

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Micro and nanoelectromechanical systems M/NEMS have been extensively investigated and exploited in the past few decades for various applications and for probing fundamental physical phenomena. Understanding the linear and nonlinear dynamical behaviors of the movable structures in these systems is crucial for their successful implementation in various novel technologies and to meet the long list of new sophisticated requirements. This paper presents a review for some of the recent topics pertaining to the dynamical behaviors, linear and nonlinear, of M/NEMS resonating structures. First, an overview is presented of the various used dynamical approaches to enhance the sensitivity of resonators for sensing applications. Then a summary is presented of the recent works on the linear and nonlinear mode coupling in M/NEMS resonator. Next, recent research is reviewed on coupled M/NEMS resonators, mechanically and electrically, leading to collective behaviors like mode localization. The final part of the paper discusses analytical approaches that have been developed to better understand and investigate the dynamical behavior of M/NEMS resonators focusing on the perturbation method the multiple time scales.

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Section: Internal Resonancementioning

confidence: 56%

“…In the past few decades, internal resonance in M/NEMS has been widely studied in various structures including cantilevers [162,163], arch beams [32,123,156], membranes from 2D material (such as graphene and MoS2) [122,142], CNTs [164], and electrically and mechanically coupled structures [31,158,161].…”

Section: Internal Resonancementioning

confidence: 99%

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Hajjaj

Jaber

Ilyas

et al. 2020

International Journal of Non-Linear Mechanics

115

View full text Add to dashboard Cite

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“…Recent works, however, have shown that a microcantilever specifically designed to realize internal resonance can trigger two modes even with single-frequency excitation. Specifically, in [73][74][75][76], a microcantilever was designed with an inner paddle, as shown in figure 6, so that the linearized frequencies of the leading bending modes of the base cantilever and the inner paddle are in a 1 : n rational relationship. When nonlinearity is included in the dynamics through the strong non-smooth nonlinear tip-sample interactions generated during the AFM tapping operation, a strong nth harmonic component is passively triggered in the response of the paddle via the internal resonance mechanism.…”

Section: Internal Resonancementioning

confidence: 99%

“…The experimental characterization of these systems has clearly shown the characteristic dynamic features due to internal resonance, exotic M-shaped resonance curve, nonlinear energy transfer and amplitude saturation, as illustrated in figure 5d-f. Autoparametric amplification was also reported in a micromechanical disc resonator due to internal resonance between the degenerate vibrational modes, when the frequencies of these modes are electrostatically tuned to match perfectly [70]. Internal resonance has also been exploited in a microcantilever design to achieve multifrequency atomic force microscopy (AFM) [71][72][73][74][75][76]. Various schemes of multifrequency AFM have been developed to characterize a sample beyond topography [22].…”

Section: Internal Resonancementioning

confidence: 99%

Nonlinear couplings and energy transfers in micro- and nano-mechanical resonators: intermodal coupling, internal resonance and synchronization

Asadi

Cho

2018

Phil. Trans. R. Soc. A.

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Extensive development of micro/nano-electromechanical systems (MEMS/NEMS) has resulted in technologies that exhibit excellent performance over a wide range of applications in both applied (e.g. sensing, imaging, timing and signal processing) and fundamental sciences (e.g. quantum-level problems). Many of these outstanding applications benefit from resonance phenomena by employing micro/nanoscale mechanical resonators often fabricated into a beam-, membrane- or plate-type structure. During the early development stage, one of the vibrational modes (typically the fundamental mode) of a resonator is considered in the design and application. In the past decade, however, there has been a growing interest in using more than one vibrational mode for the enhanced functionality of MEMS/NEMS. In this paper, we review recent research efforts to investigate the nonlinear coupling and energy transfers between multiple modes in micro/nano-mechanical resonators, focusing especially on intermodal coupling, internal resonance and synchronization.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

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“…For instance, the transfer of excessive energy through strong intermodal coupling can stabilize the frequency fluctuations in a micro/nanomechanical oscillator [28][29][30][31] and enable the detection of angular rate signals in Coriolis vibratory gyroscopes 32,33 . The IR mode can also be employed as an additional sensing channel to measure two different physical quantities simultaneously [34][35][36] . In addition, the faster energy exchange between the internal modes than that caused by the environmental source can provide an efficient route to engineering the intrinsic dissipation of an oscillator [37][38][39] .…”

Section: Introductionmentioning

confidence: 99%

Strong internal resonance in a nonlinear, asymmetric microbeam resonator

2021

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Exploiting nonlinear characteristics in micro/nanosystems has been a subject of increasing interest in the last decade. Among others, vigorous intermodal coupling through internal resonance (IR) has drawn much attention because it can suggest new strategies to steer energy within a micro/nanomechanical resonator. However, a challenge in utilizing IR in practical applications is imposing the required frequency commensurability between vibrational modes of a nonlinear micro/nanoresonator. Here, we experimentally and analytically investigate the 1:2 and 2:1 IR in a clamped–clamped beam resonator to provide insights into the detailed mechanism of IR. It is demonstrated that the intermodal coupling between the second and third flexural modes in an asymmetric structure (e.g., nonprismatic beam) provides an optimal condition to easily implement a strong IR with high energy transfer to the internally resonated mode. In this case, the quadratic coupling between these flexural modes, originating from the stretching effect, is the dominant nonlinear mechanism over other types of geometric nonlinearity. The design strategies proposed in this paper can be integrated into a typical micro/nanoelectromechanical system (M/NEMS) via a simple modification of the geometric parameters of resonators, and thus, we expect this study to stimulate further research and boost paradigm-shifting applications exploring the various benefits of IR in micro/nanosystems.

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Cantilever dynamics in higher-harmonic atomic force microscopy for enhanced material characterization

Cited by 19 publications

References 19 publications

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Linear and nonlinear dynamics of micro and nano-resonators: Review of recent advances

Nonlinear couplings and energy transfers in micro- and nano-mechanical resonators: intermodal coupling, internal resonance and synchronization

Strong internal resonance in a nonlinear, asymmetric microbeam resonator

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