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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

Sample text

Thermoclastic attenuation is proportional to the thermal conductivity of the solid and, while important in metals, is not the dominant damping mechanism in insulators used in acoustic devices. 8), 6 Tt = ~'. 17) in which the viscosity tensor ~/u has the same symmetry as the elastic stiffness tensor cls. The following example will serve to illustratehow attenuation may be predicted using this model. 17. 17 implies that attenuation may be accounted for by representing the elastic constants cu by complex elastic constants cu + jwvlu.

Mass that is rigidly bound moves synchronously with the crystal surface, perturbing the TSM resonant frequency. The relation between surface mass accumulation and resonant frequency change can be derived from a simple variational principle proposed by Rayleigh [5]: resonance in a mechanical system occurs at frequencies at which the peak kinetic energy Uk exactly balances the peak potential energy Up. This principle is a consequence of the fact that energy is periodically exchanged between kinetic and potential forms at resonance.

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. [9]. 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. Mass that is rigidly bound moves synchronously with the crystal surface, perturbing the TSM resonant frequency. The relation between surface mass accumulation and resonant frequency change can be derived from a simple variational principle proposed by Rayleigh [5]: resonance in a mechanical system occurs at frequencies at which the peak kinetic energy Uk exactly balances the peak potential energy Up.

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