Viscous damping on flexural mechanical resonators

Aoust, Guillaume; Lévy, R.; Bourgeteau, Béatrice; Traon, O. Le

doi:10.1016/j.sna.2015.04.004

Cited by 22 publications

(24 citation statements)

References 18 publications

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“…The total hydrodynamic function originates from the linearized Navier–Stokes equation. Thus, it can be represented as a linear combination of hydrodynamic functions originating from each sidewall of the beam cross-section [ 33 ]. Pictorially, it is presented in Figure 5 , while mathematically it is expressed as:

where

are hydrodynamic functions originating from the top and bottom side of the cantilever, squeeze film, and the left and right side of the cantilever, respectively.…”

Section: Damping Mechanism—quality Factormentioning

confidence: 99%

“…The theoretical approach of

can be found in [ 33 ] and takes the following form:

As explained in [ 35 ], this expression neglects edge and thickness effects, but remains a sufficient approximation in our configuration since it has been tested and compared to experimental results in [ 33 ].…”

Section: Damping Mechanism—quality Factormentioning

confidence: 99%

“…The total hydrodynamic function originates from the linearized Navier-Stokes equation. Thus, it can be represented as a linear combination of hydrodynamic functions originating from each sidewall of the beam cross-section [33]. Pictorially, it is presented in Figure 5, while mathematically it is expressed as:…”

Section: Viscous Dampingmentioning

confidence: 99%

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Analytic Optimization of Cantilevers for Photoacoustic Gas Sensor with Capacitive Transduction

Trzpil

Maurin

Rousseau

et al. 2021

Sensors

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We propose a new concept of photoacoustic gas sensing based on capacitive transduction which allows full integration while conserving the required characteristics of the sensor. For the sensor’s performance optimization, trial and error method is not feasible due to economic and time constrains. Therefore, we focus on a theoretical optimization of the sensor reinforced by computational methods implemented in a Python programming environment. We present an analytic model to optimize the geometry of a cantilever used as a capacitive transducer in photoacoustic spectroscopy. We describe all the physical parameters which have to be considered for this optimization (photoacoustic force, damping, mechanical susceptibility, capacitive transduction, etc.). These parameters are characterized by opposite trends. They are studied and compared to obtain geometric values for which the signal output and signal-to-noise ratio are maximized.

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where

are hydrodynamic functions originating from the top and bottom side of the cantilever, squeeze film, and the left and right side of the cantilever, respectively.…”

Section: Damping Mechanism—quality Factormentioning

confidence: 99%

“…The theoretical approach of

can be found in [ 33 ] and takes the following form:

Section: Damping Mechanism—quality Factormentioning

confidence: 99%

See 1 more Smart Citation

Analytic Optimization of Cantilevers for Photoacoustic Gas Sensor with Capacitive Transduction

Trzpil

Maurin

Rousseau

et al. 2021

Sensors

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show abstract

“…This fact corroborates with the reduction in stiffness coefficients [Eq. (16)] as a consequence of reduction in the Young modulus of Si. As a result for the three gases, the variation of S EM as a function of temperature is below 0.17 dB in the entire operational range, for both evaluated pressures, depending only on the silicon mechanical properties at low frequencies.…”

Section: Electromechanical Sensitivitymentioning

confidence: 99%

“…Their results show good agreement with experimental data. Recently, a new viscous damping model was proposed by Aoust et al [16] to study MEMS resonators, for which additional damping sources have become important. Although analytical SFD models for MEMS structures have received distinct contributions [12,17], and the same attention is true also in studies associated with thermoelastic features in silicon MEMS [14], the concomitant, squeeze film damping and thermoelastic mechanical effects experienced on dynamic sensitivity of MEMS accelerometers, based on analytical approach, were not tackled before according to the best of our understanding.…”

Section: Introductionmentioning

confidence: 99%

MEMS capacitive accelerometer: dynamic sensitivity analysis based on analytical squeeze film damping and mechanical thermoelasticity approaches

Silva¹,

Rodrigues²,

Passaro³

et al. 2019

SN Appl. Sci.

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In this work, we adopt a semi-analytical model to study a capacitive MEMS accelerometer based in silicon (Si). Such model takes into account the thermoelastic stiffness and linear expansion coefficients of anisotropic bulk Si. In addition, an analytical damping model, derived from the Reynolds equation, is incorporated in the model, in order to study dynamical characteristics of a MEMS capacitive accelerometer. Such approach takes into account the inertial effects on squeeze film damping in air, argon and helium gases, assumed as being ideal gases. The simulation model was compared with experimental measurements. The main figure of merit adopted is the electromechanical sensitivity (S EM), assuming frequency response and considering the effect of gas pressure, as well as temperature, on the damping loss mechanisms in such devices. The resulted model implementation shows a good agreement with the experimental data. For all gases, the sensitivity at 20 Pa presents less variation than at 200 Pa. At 20 Pa, the linear response of the device reaches up to 300 Hz, approximately, for air and helium, assuming variation of ≈ 0.5 dB, no matter which temperature. For 200 Pa, the linear response drops down to about 150 Hz. Also, for the three gases, the variation of S EM as a function of temperature is below 0.17 dB in the entire operational range, for both evaluated pressures, depending only on the silicon mechanical properties at low frequencies.

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Theoretical analysis of a resonant quartz-enhanced photoacoustic spectroscopy sensor

et al. 2017

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Viscous damping on flexural mechanical resonators

Cited by 22 publications

References 18 publications

Analytic Optimization of Cantilevers for Photoacoustic Gas Sensor with Capacitive Transduction

Analytic Optimization of Cantilevers for Photoacoustic Gas Sensor with Capacitive Transduction

MEMS capacitive accelerometer: dynamic sensitivity analysis based on analytical squeeze film damping and mechanical thermoelasticity approaches

Theoretical analysis of a resonant quartz-enhanced photoacoustic spectroscopy sensor

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