Results on the resonant electromagnetic vibrations of piezoceramic half-disks are analyzed, systematized, and generalized. Considerable attention is paid to new experimental methods for and results of studying resonant vibrations Introduction. The resonant electromechanical vibrations of a thin half-disk made of TsTS-19 piezoceramic were first described in [14] where an original method was used: the resonant frequencies of a piezoelectric element were measured from the maximum shunting effect on the output resistor of a voltage divider. As in the ordinary Meson circuit [1], the voltage divider (two series-connected resistors, 56 W and 5.6 W) is connected between a GZ-56/1 generator and the piezoelectric element. The output voltage of the generator is set so that the voltage drop across the 5.6 W resistor is 100 mV in the absence of the piezoelectric element. As the generator frequency is varied, the admittance of the piezoelectric element changes, peaking at the resonant frequencies. As a result, the voltage across the parallel-connected resistor and piezoelectric element increases by a factor of 1/K, and it becomes possible to determine the resonant admittance of the piezoelectric element and to measure its resonant frequency. In [14], resonant frequencies, admittances, and impedances for 10 vibration modes were determined. The height and azimuthal distributions of dynamic mechanical stresses obtained with the piezotransformer transducer method (PTTM) [5][6][7] were analyzed too. The antiresonance frequencies and admittances were not considered. Note that the electromechanical vibrations of piezoceramic bodies (shells and plates) were also studied in [17, 18, etc.] The present paper studies the behavior of the admittance of a piezoceramic half-disk in a frequency range that includes resonance and antiresonance frequencies, and proposes a new highly accurate experimental method to determine the admittance of piezoelectric elements at any frequency.
Advantages and Disadvantages of the Mason Circuit.After the close (in frequency) current and voltage resonances in piezoelectric elements had been experimentally discovered, it became necessary to develop a method to determine the associated frequencies. In many cases, the simple Mason circuit (Fig. 1) detailed in [1-3, 7, 8, 11] is used.The basic advantage of the Mason circuit is the possibility to measure the frequencies of maximum and minimum admittances. The shunting method [14] and PTTM [5][6][7] are incapable of doing this. These methods measure the maximum shunting frequency and the maximum piezotransformer ratio frequency, respectively. Both these frequencies are close yet unequal to the resonance frequencies. At the electromechanical resonance frequencies, piezoceramic elements behave (in relation to the external ultrasonic generator) as an oscillatory circuit, which consists of series-connected inductance coil L k , capacitor C k , and loss resistor R k . The scalar impedance Z k of this system at a circular frequency w is defined as follows [4]: