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By David Stephen Ballantine; et al

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22) Since the series resonant frequency is defined as the point where motional inductance and capacitance resonate, the motional inductance L2 causes a shift in series resonant frequency (relative to the unperturbed case) given by: Afs = L2fs 2(L! 23) The formalism outlined above will be applied to determine equivalent-circuit models for a TSM resonator with (1) an ideal mass layer, (2) a contacting semiinfinite liquid, and (3) a viscoelastic film. By determining the mechanical impedance Zs associated with each perturbation, the equivalent-circuit model arising from each can be obtained.

00 Electrical admittance vs frequency for an unloaded TSM resonator. (Reprinted with permission. See Ref. [9]. ) 50 3. Acoustic Wave Sensors and Responses proximates the electrical characteristics of the TSM resonator for excitation frequencies near resonance [9,11]. 5) can be used to describe the electrical response of the perturbed device. 5b, is most convenient to use. 7. This model contains the elements Co*, LI, Cl, and RI corresponding to the unperturbed resonator. 7a. 20) Vx lY=O where Txy is the sinusoidal steady-state shear stress (force per area in the xdirection on a y-normal plane) imposed on the contacting medium by the resonator, and Vx is the resulting x-directed surface shear particle velocity.

Sensors and Actuators, 20, 253-268 (1989). 5. Nye, J. F. Physical Properties of Crystals; Clarendon Press: Oxford (1957). 6. IEEE Standard on Piezoelectricity 176-1987; IEEE Press: Piscataway, NJ (1986). Chapter 3 ] AcousticWave Sensors and Responses Devices based on piezoelectric crystals, which allow transduction between electrical and acoustic energies, have been constructed in a number of configurations for sensor applications and materials characterization. This chapter examines those devices most commonly utilized for sensing applications, including the thicknessshear mode (TSM) resonator, the surface acoustic wave (SAW) device, the acoustic plate mode (APM) device, and the flexural plate wave (FPW) device.

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