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By David Stephen Ballantine; et al

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Extra info for Acoustic wave sensors : theory, design, and physico-chemical applications

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11), the presence of an additional term involving the electrical potential ~b is apparent. This term may be considered as a source term responsible for the generation of an acoustic wave by an applied, time-varying electrical potential, s Conversely, the wave displacements generate an accompanying electrical potential through which the piezoelectric wave can be electrically detected. 28 represents three equations in four unknowns: ul, u2, u3, and ~b. 26 by noting that in a region with no free charges, the electrical displacement is solenoidal (V • D = 0).

59) in which k0 is the unperturbed wavenumber. The latter makes clear that Aot/k and AV/Vo are consistently normalized orthogonal components of changes in the complex propagation factor 3, caused by a generalized perturbation [4]. The dependencies of these quantities on a given perturbation therefore will be the subject of numerous theoretical calculations as well as experimental measurements to be discussed in later chapters. 55 to define a complex power transfer Prfrom the wave, by the perturbation, that accounts for both power dissipation Pd and changes in stored energy AU: Pr = Pd + j2toAU.

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. , N = 1, 3, 5 . . [4]. 65 g/cm 3. 3 Transit of a shear wave, illustrating the resonant condition. 06 MHz. Having derived the condition for crystal resonance allows the displacement profile at resonance to be calculated. When the crystal is operated in air or vacuum, the crystal faces experience no external restoring force and arc considered to be stress-free boundaries; this implies that Oux/Oy = 0 at the upper and lower crystal faces.

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