The frequency response of a flat plate in a viscous fluid is a problem with applications in microsystems, including gyroscopes, accelerometers, viscometers, and biological sensing. To find the frequency response away from the resonant frequency, the equations of motion are combined with the solution to Stokes’ second problem to produce an analytic solution for the motion of the plate in response to a sinusoidal driving force. These results are used to determine the gain, phase lag, and dynamic stability of the system. The behavior of the system depends on an effective damping ratio , which depends on the resonator dimensions, and is proportional to the square root of the viscosity times the fluid density.
Issue Section:
Research Papers
Keywords:
damping,
frequency response,
mechanical stability,
plates (structures),
vibrations,
viscosity
Topics:
Damping,
Flat plates,
Fluids,
Frequency response,
Viscosity,
Resonance,
Equations of motion,
Vibration
1.
Weinberg
, M. S.
, Dube
, C. E.
, Petrovich
, A.
, and Zapata
, A. M.
, 2003, “Fluid Damping in Resonant Flexural Plate Wave Device
,” J. Microelectromech. Syst.
JMIYET 1057-7157, 12
(5
), pp. 567–76.2.
Cho
, Y. -H.
, Kwak
, B. M.
, Pisano
, A. P.
, and Howe
, R. T.
, 1994, “Slide Film Damping in Laterally Driven Microstructures
,” Sens. Actuators, A
SAAPEB 0924-4247, 40
(1
), pp. 31–39.3.
Cho
, Y. -H.
, Pisano
, A. P.
, and Howe
, R. T.
, 1994, “Viscous Damping Model for Laterally Oscillating Microstructures
,” J. Microelectromech. Syst.
JMIYET 1057-7157, 3
(2
), pp. 81–87.4.
Turowski
, M.
, Chen
, Z.
, and Przekwas
, A.
, 1999, “High-Fidelity and Behavioral Simulation of Air Damping in MEMS
,” Technical Proceedings, 1999 International Conference on Modeling and Simulation of Microsystems
.5.
Yang
, Y. -J.
, and Yu
, C. -J.
, 2002, “Macro Model Extraction of Gas Damping Effects for Perforated Surfaces With Arbitrarily-Shaped Geometries
,” Technical Proceedings, 2002 International Conference on Modeling and Simulation of Microsystems
.6.
Ye
, W.
, Wang
, X.
, Hemmer
, W.
, Freeman
, D.
, and White
, J.
, 2003, “Air Damping in Laterally Oscillating Microresonators: A Numerical and Experimental Study
,” J. Microelectromech. Syst.
JMIYET 1057-7157, 12
(5
), pp. 557–566.7.
Alper
, S. E.
, Azgin
, K.
, and Akin
, T.
, 2007, “A High-Performance Silicon-on-Insulator MEMS Gyroscope Operating at Atmospheric Pressure
,” Sens. Actuators, A
SAAPEB 0924-4247, 135
(1
), pp. 34–42.8.
Yazdi
, N.
, Ayazi
, F.
, and Najafi
, K.
, 1998, “Micromachined Interial Sensors
,” Proc. IEEE
IEEPAD 0018-9219, 86
(8
), pp. 1640–1659.9.
Lu
, C.
, Lemkin
, M.
, and Boser
, B. E.
, 1995, “A Monolithic Surface Micromachined Accelerometer With Digital Output
,” IEEE J. Solid-State Circuits
IJSCBC 0018-9200, 30
(12
), pp. 1367–1373.10.
Martin
, S. J.
, Fry
, G. C.
, and Wessendorf
, K. O.
, 1994, “Sensing Liquid Properties With Thickness-Shear Mode Resistors
,” Sens. Actuators, A
SAAPEB 0924-4247, 44
(3
), pp. 209–218.11.
Riesch
, C.
, Reichel
, E. K.
, Jachimowicz
, A.
, Schalko
, J.
, Hudek
, P.
, Jakoby
, B.
, and Keplinger
, F.
, 2009, “A Suspended Plate Viscosity Sensor Featuring In-Plane Vibration and Piezoresistive Readout
,” J. Micromech. Microeng.
JMMIEZ 0960-1317, 19
(7
), pp. 075010.12.
Kanazawa
, K. K.
, and Gordon
, J. G.
, 1985, “The Oscillation Frequency of a Quartz Resonator in Contact With a Liquid
,” Anal. Chim. Acta
ACACAM 0003-2670, 175
(1
), pp. 99–105.13.
Jae
, H. S.
, and Brand
, O.
, 2008, “High Q-Factor In-Plane-Mode Resonant Microsensor Platform for Gaseous/Liquid Environment
,” J. Microelectromech. Syst.
JMIYET 1057-7157, 17
(2
), pp. 483–493.14.
Muramatsu
, H.
, Dicks
, J. M.
, Tamiya
, E.
, and Karube
, I.
, 1987, “Piezoelectric Crystal Biosensor Modified With Protein-A for the Determination of Immunoglobins
,” Anal. Chem.
ANCHAM 0003-2700, 59
(23
), pp. 2760–2763.15.
Stokes
, G. G.
, 1851, “On the Effect of the Internal Friction of Fluids on the Motion of Pendulums
,” Cambridge Philosophical Society Transactions
, 9
, pp. 8–106.16.
Currie
, I. G.
, 1993, Fundamental Mechanics of Fluids
, 2nd ed., McGraw-Hill
, New York
.17.
Yakhot
, V.
, and Colosqui
, C.
, 2007, “Stokes’ Second Flow Problem in a High-Frequency Limit: Application to Nanomechanical Resonators
,” J. Fluid Mech.
JFLSA7 0022-1120, 586
, pp. 249–258.18.
Park
, S.
, and Horowitz
, R.
, 2003, “Adaptive Control for the Conventional Mode of Operation of MEMS Gyroscopes
,” J. Microelectromech. Syst.
JMIYET 1057-7157, 12
(1
), pp. 101–108.19.
Sung
, W. T.
, Sung
, S.
, Lee
, J. -Y.
, Kang
, T.
, Lee
, Y. J.
, and Lee
, J. G.
, 2008, “Development of a Lateral Velocity-Controlled MEMS Vibratory Gyroscope and Its Performance Test
,” J. Micromech. Microeng.
JMMIEZ 0960-1317, 18
(5
), p. 055028.20.
Franklin
, G. F.
, Powell
, J. D.
, and Emani-Naeini
, A.
, 2003, Feedback Control of Dynamic Systems
, 4th ed., Prentice-Hall
, Upper Saddle River, NJ
.21.
Nguyen
, C. T.-C.
, and Howe
, R. T.
, 1999, “An Integrated CMOS Micromechanical Resonator High-Q Oscillator
,” IEEE J. Solid-State Circuits
IJSCBC 0018-9200, 34
(4
), pp. 440–455.22.
Hoppensteadt
, F. C.
, and Izhikevich
, E. M.
, 2001, “An Integrated CMOS Micromechanical Resonator High-Q Oscillator
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
ITCAEX 1057-7122, 48
(2
), pp. 133–138.23.
Martin
, M. J.
, and Houston
, B. H.
, 2011, “Frequency Response of Cylindrical Resonators in a Viscous Fluid
,” ASME J. Vibr. Acoust.
JVACEK 0739-3717, 133
(3
), 031009 (2011).24.
Larson
, R. E.
, Hostetler
, R. P.
, and Edwards
, B. H.
, 1990, Calculus With Analytic Geometry
, 4th ed., D. C. Heath and Company
, Lexington, MA
.25.
Thompson
, W. T.
, 1993, Theory of Vibrations With Applications
, Prentice-Hall
, Englewood Cliffs, NJ
.Copyright © 2011
by American Society of Mechanical Engineers
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