Revisiting the Modeling of the Vibrations of High-Power Piezoceramic Resonators Using an Equivalent Circuit
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International Applied Mechanics, Vol. 56, No. 2, March, 2020
REVISITING THE MODELING OF THE VIBRATIONS OF HIGH-POWER PIEZOCERAMIC RESONATORS USING AN EQUIVALENT CIRCUIT
V. L. Karlash
We estimated different Van Dyke equivalent circuits for low and high power levels. The R, C, L model is compared and matched with AFC of the radial vibrations of a piezoelectric disk. The proposed conception of taking into account only constant (frequency-independent) values of dielectric, elastic, and piezoelectric loss tangents does not conflict with the analytical and experimental results. The additional loss resistor, under high power conditions, has less influence at the resonance than at the antiresonance and must be connected in series with clamped shunting capacity. Keywords: piezoceramic resonators, energy losses, equivalent circuit, R, C, L models, efficiency Introduction. The vibrations of piezoceramic structural elements have their own characteristics. They are distinguished by strong coupling of strains and electric-field strength [1, 3, 4, 11–13, 16, 21]. To calculate the amplitudes of displacements, strains, and stresses, it is necessary to take into account energy losses [7–10, 16, 27, 28], which are currently considered to have mechanical, dielectric, and piezoelectric components [18, 29, 31–36]. Energy losses are especially significant at high frequencies and at significant powers [24, 32, 35]. Approximate formulas are derived in the monograph [14]. These formulas relate the energy loss tangents to the maxima and minima of the admittance for several samples specially made as rods and plates. Similar issues of energy loss in piezoceramic resonators were studied in [2, 9, 13, 24, 24 – 26, 14, 17, 26, etc.]. They show that the study of energy losses during the vibrations of piezoceramic bodies will be relevant for a long time. The present paper compares experimental data obtained from an equivalent circuit consisting of arbitrarily selected R, C, L passive elements and during forced vibrations of a real piezoceramic disk. Experiments with R, C, L models make it possible to assert that the Van Dyke equivalent circuit [37], proposed more than 90 years ago, gives a physical explanation of the results obtained by modern authors. The author’s concept of taking into account only constant (frequency-independent) values of the tangents of dielectric, elastic, and piezoelectric losses does not contradict either analytical or experimental data. 1. The Effect of Energy Losses on Admittance. A noticeable difference between the constant-current and constant-voltage modes is observed in high-power ultrasonic devices such as radiators, motors, or transformers [3, 11, 34–36]. It was shown in [36] without explanation, that the constant voltage is accompanied by high nonlinearity of the admittance-frequency characteristics near resonances, up to jumps, whereas such nonlinearity is not observed at constant current. We consider that there are severe difficulties in determining the electromechanical-coupling parameters under high electric
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