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Title: Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance

Abstract

We derive a lumped-element, equivalent-circuit model for the thickness shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of {pi}/2 radians. This model predicts accurately the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. The elements of the model are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and the Sauerbrey models.

Authors:
; ; ; ;
Publication Date:
Research Org.:
Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
12678
Report Number(s):
SAND99-2411J
TRN: AH200120%%384
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
Analytical Chemistry
Additional Journal Information:
Other Information: Submitted to Analytical Chemistry; PBD: 16 Sep 1999
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ACOUSTICS; DAMPING; PHASE SHIFT; QUARTZ; RESONANCE; RESONATORS; SHEAR; THICKNESS; MATHEMATICAL MODELS; VISCOSITY; ELASTICITY; THICKNESS-SHEAR MODE RESONATOR; QUARTZ CRYSTAL MICROBALANCE; VISCOELEASTICITY; FILM RESONANCE; EQUIVALENT CIRCUIT; LUMPED-ELEMENT MODEL; TRANSMISSION-LINE MODEL

Citation Formats

BANDEY, HELEN L., BROWN, MARK J., CERNOSEK, RICHARD W., HILLMAN, A. ROBERT, and MARTIN, STEPHEN J. Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance. United States: N. p., 1999. Web.
BANDEY, HELEN L., BROWN, MARK J., CERNOSEK, RICHARD W., HILLMAN, A. ROBERT, & MARTIN, STEPHEN J. Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance. United States.
BANDEY, HELEN L., BROWN, MARK J., CERNOSEK, RICHARD W., HILLMAN, A. ROBERT, and MARTIN, STEPHEN J. Thu . "Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance". United States. https://www.osti.gov/servlets/purl/12678.
@article{osti_12678,
title = {Equivalent-Circuit Model for the Thickness-Shear Mode Resonator with a Viscoelastic Film Near Film Resonance},
author = {BANDEY, HELEN L. and BROWN, MARK J. and CERNOSEK, RICHARD W. and HILLMAN, A. ROBERT and MARTIN, STEPHEN J.},
abstractNote = {We derive a lumped-element, equivalent-circuit model for the thickness shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of {pi}/2 radians. This model predicts accurately the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. The elements of the model are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and the Sauerbrey models.},
doi = {},
journal = {Analytical Chemistry},
number = ,
volume = ,
place = {United States},
year = {1999},
month = {9}
}