# definition pezomodulja a resonance-antiresonance method

For definition pezomodulja the method of a resonance - of a parallel resonance is used. The Block diagramme of corresponding observational installation is presented on fig. 2.1 [175]. If on a piezoelectric crystal to put a variable electric field under the influence of this field the crystal will make forced oscillations [176].

Variable electrical oscillations from the generator 1 move on the piezoelectric device 2 consistently joined to resistance R-IOO the Ohm. The voltage on resistance is measured by a tube voltmeter 3. Frequency of electrical oscillations is measured by a frequency metre 4.

Fig. 2.1. The Block diagramme of the observational installation for definition pezomodulej a resonance-antiresonance method: 1 - the generator;

2 - a piezoelectric device; 3 - a tube voltmeter; 4 - a frequency metre

Character of behaviour of a piezoelectric crystal near to a resonant frequency is analyzed on the basis of viewing of the equivalent

To it of a circuitry [175-177]. While frequency of weeding is much less than frequency of eigentones of a crystalline plate, the vibration amplitude is small. However when frequency comes nearer to frequency of eigentones of a plate, the amplitude sharply increases. Hence, the electrical energy consumed pezorezonatorom is incremented also, i.e. the electric current flowing through the piezoelectric resonator 2 increases, reaching the peak value at a resonant frequency f_{r}. At the further magnification of frequency of a master oscillator frequency f_{a}, termed antiresonant at which full resistance of a dual circuit (impedance) becomes peak, and a current in a chain - underload is reached. On a maximum and a current minimum in a chain it is possible to register frequencies of a resonance f_{r}и a parallel resonance f_{a}. These frequencies are spotted by the sizes, elastic, dielectric and piezoelectric properties pezorezonatora. They are related as a first approximation to an electromechanical force factor a relation:

gdeesli there is the transformation of energy related with 1st

komponentoj an electric field and j-й komponentoj strains the electromechanical force factor is expressed by a relation (in system SGS):

Where - piezoelectric modules by which it is featured

Piezoelectric excitation, - an inductivity of mechanically free crystal, - the operating coefficients of an elastic compliance measured at a constant electric field.

Resonance-antiresonance method it is possible to spot elastic constants by measuring of an impedance of a crystal in a wide frequency band [176-178]. The lowest and highest frequencies of a resonance are calculated under formulas: where / - chastotozadajushchy the size of a plate or the size of the leg along which there are crystal oscillations, - values of coefficient

Elastic compliance, r - density.

Evaluation du is yielded under the formula (vsi):

Where ε_{2} - an inductivity, ε_{0} - a permittivity of vacuum, Cn and Cu elastic constants. According to Г361

2.2.

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