Nonlinear dynamics of micromechanical resonator arrays for mass sensing

Baguet, Sébastien; Nguyen, van Nghi; Grenat, Clément; Lamarque, Claude‐Henri; Dufour, Régis

doi:10.1007/s11071-018-4624-0

Cited by 41 publications

(20 citation statements)

References 32 publications

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“…An electrically actuated microbeam structure has important applications in MEMS mass sensors [ 1 ]. The mass added to the microbeam can result in downshifting its natural frequency.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Recently, mass detection of very small chemical and biological species using microelectromechanical systems (MEMS) has attracted wide attention [ 1 , 2 , 3 , 4 , 5 , 6 ]. A MEMS mass sensor mainly uses the mechanical characteristics changes before and after the adsorption mass of a resonant element to detect and identify the target analyte [ 7 ].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

Liu

Shao

et al. 2021

Micromachines

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Frequency stabilization can overcome the dependence of resonance frequency on amplitude in nonlinear microelectromechanical systems, which is potentially useful in nonlinear mass sensor. In this paper, the physical conditions for frequency stabilization are presented theoretically, and the influence of system parameters on frequency stabilization is analyzed. Firstly, a nonlinear mechanically coupled resonant structure is designed with a nonlinear force composed of a pair of bias voltages and an alternating current (AC) harmonic load. We study coupled-mode vibration and derive the expression of resonance frequency in the nonlinear regime by utilizing perturbation and bifurcation analysis. It is found that improving the quality factor of the system is crucial to realize the frequency stabilization. Typically, stochastic dynamic equation is introduced to prove that the coupled resonant structure can overcome the influence of voltage fluctuation on resonance frequency and improve the robustness of the sensor. In addition, a novel parameter identification method is proposed by using frequency stabilization and bifurcation jumping, which effectively avoids resonance frequency shifts caused by driving voltage. Finally, numerical studies are introduced to verify the mass detection method. The results in this paper can be used to guide the design of a nonlinear sensor.

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“…An electrically actuated microbeam structure has important applications in MEMS mass sensors [ 1 ]. The mass added to the microbeam can result in downshifting its natural frequency.…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

Liu

Shao

et al. 2021

Micromachines

View full text Add to dashboard Cite

show abstract

“…( 1)-( 4) to remove the hats. Assuming that the device operates under moderate amplitude vibrations, the electrostatic excitation force term is expended to third-order Taylor series [28,29].…”

Section: Nondimensionalizationmentioning

confidence: 99%

An asymmetric mode-localized mass sensor based on the electrostatic coupling of different structural modes with distributed electrodes

Song

Lyu

Kacem

et al. 2021

Preprint

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Mode-localization sensor with amplitude ratio as output metric has shown excellent potential in the field of micro-mass detection. In this paper, an asymmetric mode -localized mass sensor with a pair of electrostatically coupled resonators of different thickness is proposed. Partially distributed electrodes are introduced to ensure the asymmetric mode coupling of second and third order modes while actuating the thinner resonator by the distributed electrode. The analytical dynamic model is established by Euler–Bernoulli theory and solved by harmonic balance method (HBM) combined with asymptotic numerical method (ANM). Detailed investigations on the linear and nonlinear behavior, critical amplitude as well as the sensitivity of the sensor are performed. The sensitivity of the proposed sensor can be enhanced by about 20 times compared to first order mode-localized mass sensors. Furthermore, by exploiting the nonlinearities while driving the device beyond the critical amplitude for the in-phase mode, the sensor performs a great improvement in sensitivity up to 1.78 times. Besides, the influence of the decrease of coupling voltage is studied, which gives a good reference to avoid mode aliasing.

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“…The detailed derivation process is given in "Appendix B". In this paper, pseudo-trajectory processing method is introduced to solve Equations (17) and (18).…”

Section: Perturbation Analysismentioning

confidence: 99%

“…The mode coupled vibration can introduce rich nonlinear phenomena into the MEMS research and reveal the mechanism of the complex dynamic behaviors [14][15][16][17][18]. Anti-symmetric response can be induced by the mode coupled vibration.…”

Section: Introductionmentioning

confidence: 99%

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped–Clamped Microbeams for Mass Sensing

Zhang

et al. 2019

Micromachines

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This paper details study of the anti-symmetric response to the symmetrical electrostatic excitation of a Micro-electro-mechanical-systems (MEMS) resonant mass sensor. Under higher order mode excitation, two nonlinear coupled flexural modes to describe MEMS mass sensors are obtained by using Hamilton’s principle and Galerkin method. Static analysis is introduced to investigate the effect of added mass on the natural frequency of the resonant sensor. Then, the perturbation method is applied to determine the response and stability of the system for small amplitude vibration. Through bifurcation analysis, the physical conditions of the anti-symmetric mode vibration are obtained. The corresponding stability analysis is carried out. Results show that the added mass can change the bifurcation behaviors of the anti-symmetric mode and affect the voltage and frequency of the bifurcation jump point. Typically, we propose a mass parameter identification method based on the dynamic jump motion of the anti-symmetric mode. Numerical studies are introduced to verify the validity of mass detection method. Finally, the influence of physical parameters on the sensitivity of mass sensor is analyzed. It is found that the DC voltage and mass adsorption position are critical to the sensitivity of the sensor. The results of this paper can be potentially useful in nonlinear mass sensors.

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Nonlinear dynamics of micromechanical resonator arrays for mass sensing

Cited by 41 publications

References 32 publications

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

A Novel Frequency Stabilization Approach for Mass Detection in Nonlinear Mechanically Coupled Resonant Sensors

An asymmetric mode-localized mass sensor based on the electrostatic coupling of different structural modes with distributed electrodes

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped–Clamped Microbeams for Mass Sensing

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