By D. S. Ballantine Jr., Robert M. White, S. J. Martin, Antonio J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Moises Levy, Richard Stern
Written via an interdisciplinary staff of specialists from either and academia, this publication offers an in-depth examine the present nation of acoustic wave units and the scope in their use in chemical, biochemical, and actual measurements, in addition to in engineering functions. due to the inherent interdisciplinary purposes of those units, this ebook might be beneficial for the chemist and biochemist attracted to the use and improvement of those sensors for particular purposes; engineer serious about the layout and development of those units; the chemical engineer and the biotechnologist drawn to utilizing those units for strategy tracking and keep watch over; and the sensor neighborhood at huge.
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Additional info for Acoustic Wave Sensors - Theory, Design, and Physico-Chemical Applications
In equation form, the use of reduced index notation is signified by the use of capital subscripts, as St and TI. The symmetry properties that allow reduction of the number of entries in the stress and strain tensors also allow reduction of the number of elastic stiffness constants cqkt in the stiffness matrix. 1, results in a stiffness matrix requiring only 36 entries in reduced notation: ctj, where I and J range from 1 to 6. 7 is more succinctly expressed as  6 T! = Z ctjSj. 8) J=l The stiffness matrix is also symmetric with respect to the interchange of reduced indices 1 and J so that for the most general solid, 21 distinct entries (6 diagonal and 15 triangular entries) are required to completely characterize the solid.
R phase shift) and is once again propagating downward having experienced a total round-trip phase shift of (2khs + 2~br), where hs is the thickness of the crystal. , coherence) between the incident and return waves leads to crystal resonance. 2b) where N is an integer. 2a indicates that resonances occur when the crystal thickness hs is a multiple of half the acoustic wavelength A. 3) where/~qand pq are the shear stiffness and mass density, respectively. 2b indicates the frequencies at which the family of resonances can be excited, corresponding to various values of the mode index N.
Note that these modes do not involve any change in the thickness of the substrate. 33 mm, these modes are excited at approximately 5 and 15 MHz, respectively. 42 3. Acoustic Wave Sensors and Responses j N=I Y 1 I I I • " " I:. I [ I I I i t I • • t ! -- ! I Y .... :::: i • • . . ~j . 4 Shear displacement profiles across the resonator thickness for the fundamental and the third-harmonic r e s o n a n c e s . (Reprinted with permission. See Ref. . 1 43 TSM RESONATOR MASS SENSITIVITY The presence of displacement maxima at the crystal surfaces makes the thickness-shear mode very sensitive to surface mass accumulation.
Acoustic Wave Sensors - Theory, Design, and Physico-Chemical Applications by D. S. Ballantine Jr., Robert M. White, S. J. Martin, Antonio J. Ricco, E. T. Zellers, G. C. Frye, H. Wohltjen, Moises Levy, Richard Stern
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