Multimode Nonlinear Coupling Induced by Internal Resonance in a Microcantilever Resonator

Luo, Wenyao; Gao, Naikun; Liu, Duo

doi:10.1021/acs.nanolett.0c04301

Cited by 11 publications

(5 citation statements)

References 46 publications

(72 reference statements)

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“…The most common method of intermode coupling is parametric coupling. [26] In parametric coupling, two modes are coupled through a pump tone at the frequency difference, further the modes experience each other's oscillations as resonant forces. The internal resonance, the nonlinearities coupling two or more vibrational modes with an integer ratio of their resonance frequencies, is a special kind of intermode coupling that can be achieved via parametric pump [27] or the other method.…”

Section: Intermode Couplingmentioning

confidence: 99%

Mode Coupling in Electromechanical Systems: Recent Advances and Applications

Guo

Fang

Chen

et al. 2023

Adv Elect Materials

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Mode interactions have recently become the focus of intense research in micro/nanoelectromechanical systems (M/NEMS) due to their ability to improve device performance and explore the frontiers of fundamental physics. Understanding and controlling coupling between vibrational modes are critical for the development of advanced M/NEMS devices. This review summarizes the recent advances in studies of coupling between multiple modes in M/NEMS resonators, focusing especially on experimental developments and practical applications. First, depending on spatial distribution of interacting modes, this review divides the coupled mechanism in three types: intermode, near‐neighbor, and long‐range coupling. Then, several fundamental physics approaches based on mechanical‐mode coupling, including linear and nonlinear coupling, modal localization, synchronization, and phonon manipulation are reviewed. This review also introduces sensing applications by using coupled mechanical modes. Finally, the state‐of‐the‐art open questions and challenges are reviewed.

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Section: Intermode Couplingmentioning

confidence: 99%

Mode Coupling in Electromechanical Systems: Recent Advances and Applications

Guo

Fang

Chen

et al. 2023

Adv Elect Materials

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“…Internal resonance can also be found in a single cantilever beam due to its third and fourth bending modes being naturally close to a ratio of 1:2. Luo et al [21] investigate the nonlinear dynamics of multimode internal coupling in a microcantilever beam and its potential.…”

Section: Possible Use Of Internal Resonance In Structural Dynamicsmentioning

confidence: 99%

“…Luo et al. [21] investigate the nonlinear dynamics of multimode internal coupling in a microcantilever beam and its potential.…”

Section: Possible Use Of Internal Resonance In Structural Dynamicsmentioning

confidence: 99%

Internal resonance in nonlinear structures—and what it can be used for

Tatzko

2023

Proc Appl Math and Mech

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In vibrating structures, nonlinear effects can play a decisive role. For example, stiffening responses can occur in integral components with low damping, but softening effects with a shift of the resonance to lower values by an increase of the vibration energy can be observed. Often these systems are considered only in a characteristic nonlinear vibration mode, allowing well‐known phenomena to be investigated. However, it may be the case that more than one nonlinear mode has a significant effect on the structural response of multi‐degree‐of‐freedom systems. If these modes take on integer multiples of frequency values, we speak of an internal resonance. In this work, the phenomenon of internal resonance is explained on the basis of a two‐mass oscillator. For this purpose, nonlinear modal analysis (NMA) is used to determine the amplitude‐dependent behavior of the resonant frequencies, referred to as nonlinear modes. These nonlinear modes already display the internal resonance in the form of characteristic trajectories, which are examined and explained in more detail here. A computational framework consisting of harmonic balance and continuation is used to calculate the nonlinear mode curves. In addition, nonlinear frequency responses are determined and their trajectories and properties in the internal resonance region are shown. To further understand the oscillatory behavior time plots are considered. Finally, a possible use for the observed properties is discussed as well and current approaches in research for the use of internal resonances are pointed out.

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“…The coupling resonance of MEMS has become one of the hot topics in research. The nonlinear coupling and energy transfers between multiple modes in micro/nanomechanical resonators were studied on intermodal coupling, internal resonance and synchronization [19][20][21][22][23]. Multimode nonlinear coupling was achieved by (1:2) internal resonance and parametric excitation with efficient coherent energy transfer [20].…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear coupling and energy transfers between multiple modes in micro/nanomechanical resonators were studied on intermodal coupling, internal resonance and synchronization [19][20][21][22][23]. Multimode nonlinear coupling was achieved by (1:2) internal resonance and parametric excitation with efficient coherent energy transfer [20]. The influence of residual stress on the modal characteristics of MEMS resonator array was analyzed with the laser Doppler method [21].…”

Section: Introductionmentioning

confidence: 99%

Internal Resonance of the Coupling Electromechanical Systems Based on Josephson Junction Effects

Liu

Zhang

2022

Micromachines

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The internal resonances of the coupling vibration among electro-dynamic modes of an NEMS are studied for the coupling resonators connected on a Josephson junction. The methodology adopted involves coupling a resonator connected on a Josephson junction. The mathematical model of the coupled system is then obtained by considering the regulatory nonlinear effect of the phase difference of that Josephson junction. The resulting dynamic differential equation is deduced by considering the nonlinear terms of the Josephson junction and the nanobeam. The multi-scale method is then used to obtain the 1:1:1 resonant amplitude–frequency response equation of the coupled electromechanical system. The influence of the phase difference of the Josephson junction, magnetic field, external excitation and other factors are analyzed based on the internal resonant amplitude of the coupled system. The simulation results illustrate that the changes in the values of the magnetic field, excitation amplitude and divided resistances can lead to a remarkable change in the values of the nanobeam frequency and amplitude. The internal resonance principle is used to generate a mutual conversion and amplification among electrical signals and mechanical signals. This research provides a theoretical framework and a numerical approach for improving the sensitivity of magnetic quality detection.

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Multimode Nonlinear Coupling Induced by Internal Resonance in a Microcantilever Resonator

Cited by 11 publications

References 46 publications

Mode Coupling in Electromechanical Systems: Recent Advances and Applications

Mode Coupling in Electromechanical Systems: Recent Advances and Applications

Internal resonance in nonlinear structures—and what it can be used for

Internal Resonance of the Coupling Electromechanical Systems Based on Josephson Junction Effects

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