Nonlinear coupling of transverse modes of a fixed–fixed microbeam under direct and parametric excitation

Kambali, Prashant N.; Pandey, Ashok Kumar

doi:10.1007/s11071-016-3114-5

Cited by 11 publications

(4 citation statements)

References 22 publications

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“…Our calculations show that the static deflection of the beam due to gravity is of the order of few tens of nm, which is much less than the beam thickness, and can therefore be neglected. In general, due to the interaction and capacitive coupling between the PP and the S electrodes, the resulting electrostatic force acting on the beam cannot be calculated just by simply superimposing the forces f PP , equation ( 2) and f S , equation (1) [32,44]. However, to highlight the role of the interplay between the leading factors that influence the device response in the framework of the simplest possible model, we disregard the interaction and consider the contribution of each of these forces separately, as reflected by equation (3).…”

Section: Model and Operational Principlementioning

confidence: 99%

“…Fringing field electrostatic actuation was previously shown to be useful for different purposes [27][28][29][30]. Efficient parametric excitation and frequency tuning in fringing-field actuated micromechanical beams were explored in [20,[31][32][33][34]. Repulsive fringing-field electrostatic forces were implemented for energy harvesting [35], and for operation of microswitches [36], micromirrors [37,38], and microphones [39].…”

Section: Introductionmentioning

confidence: 99%

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Micromechanical resonant cantilever sensors actuated by fringing electrostatic fields

Krakover

Ilić

Krylov

2022

J. Micromech. Microeng.

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We report on the architecture and operational principle of a resonant cantilever-type displacement sensor. The device is actuated electrostatically by a side electrode that is coplanar with the cantilever and by a gap closing electrode positioned underneath the beam. The unique electrode geometry combined with the appropriate actuating voltages allows positioning of the cantilever in close proximity to the bistability threshold, where the frequency sensitivity to the electrode displacement is enhanced. Using a reduced order (RO) model backed by numerical simulations, the dependencies of the device frequency on the beam’s deflections and the actuation voltages were mapped. We show wide-range tunability that spans a range between softening and hardening behavior. We demonstrate displacement sensing using fabricated single crystal silicon ≈ 2000 m long, ≈ 5 m thick cantilevers. When compared to a resonant cantilever sensor actuated solely by a gap closing electrode, measurements from our fringing field actuated devices show a four times higher sensitivity of ≈ 98 Hz/m. The suggested approach may find applications in a broad range of micro and potentially nano-scale applications including resonant inertial, force, mass and bio-sensors.

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Section: Model and Operational Principlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Micromechanical resonant cantilever sensors actuated by fringing electrostatic fields

Krakover

Ilić

Krylov

2022

J. Micromech. Microeng.

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“…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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“…Then, transforming the dimensionless parameters to the practical ones, we obtain the displacement amplitudes of the modes|x 1 | and |x 2 |, which are implicitly given by = ω d1 − ω 1 and δ 2 = ω d2 − ω 2 are the detuning parameters of the driving forces. The amplitude-frequency responses of the coupled nonlinear modes can be simulated by calculating |x 1 | and |x 2 | with different values of ω d1 and ω d2 .It should be noted that the results of frequency responses may contain unstable branches, which can be handled with various common methods[18,33,34]. Based on above results, the resonant frequency of one mode can be modulated by the vibration of the other mode.…”

mentioning

confidence: 99%

Electrostatic nonlinear dispersive parametric mode interaction

et al. 2022

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Understanding and controlling the nonlinear coupling in micro/nanomechanical resonators are of great importance to the exploitation of advanced devices. The recently observed electrostatic nonlinear parametric coupling is a very interesting topic. However, the theoretical model of the electrostatic parametric coupling still remains unclear. This paper explicitly derives the model and the electrostatically induced dispersive parametric coupling which reveals the ability of tuning the bifurcation topology of capacitive resonators is analyzed based on the multiple-time-scale method. A novel displacement-to-frequency transduction scheme based on this electrostatic dispersive parametric coupling effect is proposed. The transduction sensitivity is theoretically given, which indicates that this electrostatic dispersive transduction scheme can provide even more design freedoms than the existing displacement-to-frequency transduction scheme based on tension modulation. In addition, a bifurcation reversal effect is predicted in the strong actuated states of the dispersive parametric coupled system, which reveals the ability of tuning the bifurcation topology of capacitive resonators.

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Nonlinear coupling of transverse modes of a fixed–fixed microbeam under direct and parametric excitation

Cited by 11 publications

References 22 publications

Micromechanical resonant cantilever sensors actuated by fringing electrostatic fields

Micromechanical resonant cantilever sensors actuated by fringing electrostatic fields

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

Electrostatic nonlinear dispersive parametric mode interaction

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