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

Asadi, Keivan; Yu, Jun; Cho, Han Na

doi:10.1098/rsta.2017.0141

Cited by 63 publications

(37 citation statements)

References 97 publications

(126 reference statements)

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“…Recently, there have been considerable theoretical and experimental works that investigate the linear and nonlinear dynamics of M/NEMS and their exploitation for various applications; many of which were surveyed in [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

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

119

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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: Introductionmentioning

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

119

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“…However, the exact origin of these modes remains an open question. Intermodal coupling normally occurs in the presence of strong non-linearity, which can be caused by intrinsic (e.g., material, geometry, actuation, detection) properties of the system or be purposely introduced to exploit the non-linear regime [25,26]. On the other hand, the observed mode shapes in this study might only be "local normal modes", which originate from a non-uniaxial stress field of the relatively wide strings used in this study.…”

Section: Discussionmentioning

confidence: 99%

Temperature-Modulated Micromechanical Thermal Analysis with Microstring Resonators Detects Multiple Coherent Features of Small Molecule Glass Transition

Karl

Thamdrup

Rantanen

et al. 2020

Sensors

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Micromechanical Thermal Analysis utilizes microstring resonators to analyze a minimum amount of sample to obtain both the thermal and mechanical responses of the sample during a heating ramp. We introduce a modulated setup by superimposing a sinusoidal heating on the linear heating and implementing a post-measurement data deconvolution process. This setup is utilized to take a closer look at the glass transition as an important fundamental feature of amorphous matter with relations to the processing and physical stability of small molecule drugs. With an additionally developed image and qualitative mode shape analysis, we are able to separate distinct features of the glass transition process and explain a previously observed two-fold change in resonance frequency. The results from this setup indicate the detection of initial relaxation to viscous flow onset as well as differences in mode responsivity and possible changes in the primary resonance mode of the string resonators. The modulated setup is helpful to distinguish these processes during the glass transition with varying responses in the frequency and quality factor domain and offers a more robust way to detect the glass transition compared to previously developed methods. Furthermore, practical and theoretical considerations are discussed when performing measurements on string resonators (and comparable emerging analytical techniques) for physicochemical characterization.

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“…Among the various nonlinear characteristics, one remarkable category belongs to intermodal coupling and nonlinear energy transfer, where two or more vibrational modes interact with each other 5,27 . The intermodal coupling strength can be significantly enhanced when the following conditions for the so-called internal resonance (IR) are satisfied in a nonlinear system: (i) the resonant frequencies of distinct vibrational modes are commensurate or nearly commensurate with each other; (ii) a proper type of nonlinearity in accordance with frequency commensurability exists 5 .…”

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

Cited by 63 publications

References 97 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

Temperature-Modulated Micromechanical Thermal Analysis with Microstring Resonators Detects Multiple Coherent Features of Small Molecule Glass Transition

Strong internal resonance in a nonlinear, asymmetric microbeam resonator

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