An indirect method to measure the variation of elastic constant c33 of piezoelectric ceramics shunted to circuit under thickness mode

• A simply model is established to measure the variations of elastic and damping constants of piezoelectric discs under shunted circuits.
• The model is analyzed by equivalent circuit theory and finite element method.
• Experiments are conducted to examine the model by an impedance analyzer.

Academic interest in the use of piezoelectric shunt damping technology in the field of vibration and noise control has been on the rise in recent years. The experimental observation of the variation of elastic constants of piezoelectric materials shunted to different circuits is a fundamental problem of this technology. The existing methods to measure the elastic constants of piezoelectric ceramics are either unsuited or complicated for such a purpose. In this paper, a modified resonator measurement method is proposed to indirectly measure the variation of elastic constant c33 of piezoelectric ceramics shunted to circuit under thickness mode. The main idea is transforming the change of c33 into the change of the electrical resonant frequency of a single-oscillator model which is easier to be observed. Mason equivalent circuit and ANSYS finite element simulation are employed for the analysis of the admittance and resonant frequency of the proposed system. Based on the proposed method, the variation of the elastic constant c33 has been investigated when the piezoelectric ceramic wafer (PZT-5H) is shunted to a resistor, a capacitor, and a resistor connected in series with an inductor respectively. The variations of the resonant frequency measured in the experiment are highly consistent with those of c33. Besides, the measurement of variation of mechanical loss factor with a shunt resistor is also discussed in this paper.