Piezoelectric stiffening increases the wave velocity from that obtained in the non-piezoelectric case. Wave velocity is given by v = (c js/p). Since the factor has a value of [Pg.28]

Piezoelectricity and piezoelectric stiffening are rigorously accounted for in the Mason circuit. This is not the case for the mathematical and optical approaches at the level of detail presented here. [Pg.73]

Circuit element related piezoelectric stiffening Acoustic impedance of a liquid, 2]iq = (icyjjp) [Pg.51]

Fig. 1 Equivalent circuit representation of the quartz crystal including a load. Piezoelectric stiffening (described by the element 42 in Fig. 13, Chap. 2 in this volume) was neglected. The sample is represented by the load Zl |

From a constitutive relation of the form t = t(D, ri) (here t is stress not time) it can be readily shown that, since there is no change in electric displacement in an open-circuit, thick-sample configuration, there are no secondary stresses due to electromechanical coupling. Nevertheless, the wavespeed is that of a piezoelectrically stiffened wave. [Pg.77]

Equation 52 shows that the areal mass density of the crystal is the only parameter connecting the load and the frequency shift, as long as the latter is small. The stiffness of the crystal (and piezoelectric stiffening, in particular) is of no influence at this level of approximation. Comparing Eqs. 51 and 39, we find [Pg.76]

Even though a/ii is an entirely acoustic quantity, the series resonance frequency is affected by the value of the electrical capacitance, Co, because of the element Z = - (j) /(icoCo), which introduces piezoelectric stiffening into the acoustic branch. Piezoelectricity adds a negative capacitor into the mechanical branch of the circuit. [Pg.71]

Anyone who is not particularly interested in (high-frequency) electrochemistry is strongly advised to ground the front electrode well before starting a QCM experiment. Otherwise the electric boundary conditions will affect A/ and AT via piezoelectric stiffening. Such effects are left aside in the discussion next. [Pg.288]

See also in sourсe #XX -- [ Pg.448 ]

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