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for the viscous fluid. We can now obtain the formula for the viscosity of the fluid:

By neglecting the small quantities of the order of e in the obtained formula, we get

The viscosity should be measured using the tangential resonance frequencies of the piezoelement. We should (1) measure the resonance frequency in the air, (2) measure the same frequency in the fluid, and (3) compute the fluid viscosity by equation 32.1 or equation 32.2.

It is difficult to excite such vibrations by a mechanical load while the electric energy in a specially chosen piezoelement can provoke vibrations in the plane of the element.

We consider the tangential vibrations of the piezoceramic plates and shear or twist vibrations of piezoceramic cylindrical shell. For example, a plate with

FIGURE 27. Piezoceramic circular piale with electrode-covered faces

TABLE 4.

The first resonance frequency as a function of plate sizes in vacuum and in glycerine

TABLE 4.

The first resonance frequency as a function of plate sizes in vacuum and in glycerine

r = 0.01 m |
r = 0.01 m |
r = 0.02 m |
r = 0.02 m | |

Hz |
2h = 0 .0005 m |
2h = 0.001 m |
2It = 0.0005 m |
2/i = 0.001 m |

U)v |
114906. |
114906. |
57453.2 |
57453.2 |

"f |
110513. |
112645. |
54417.5 |
55873.6 |

thickness polarization (with radius R and thickness 2h) performs such vibrations under the effect of an electrical load applied to the electrodes on its faces (see Figure 27). The problem was solved in Section 30. In order to illustrate this theory, we compute the first resonance frequency of a plate made of PZT-4 piezoceramic in vacuum ujv and glycerine u>f. The results can be found in Table 4.

Let us consider one more example of a circular cylindrical shell (with radius R, length 21, and thickness 2/t) polarized in the circular direction (Figure 28). The twist vibrations are exited by an electrical load applied to the electrodes on the ends. The conditions at the free electrode-covered edges are written as

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