Singular variation property of elastic constants of piezoelectric ceramics shunted to negative capacitance

Piezoelectric shunt damping has been widely used in vibration suppression, sound absorption, noise elimination, etc. In such applications, the variant elastic constants of piezoelectric materials are the essential parameters that determine the performances of the systems, when piezoelectric materials are shunted to normal electrical elements, i.e., resistance, inductance and capacitance, as well as their combinations. In recent years, many researches have demonstrated that the wideband sound absorption or vibration suppression can be realized with piezoelectric materials shunted to negative capacitance. However, most systems using the negative-capacitance shunt circuits show their instabilities in the optimal condition, which are essentially caused by the singular variation properties of elastic constants of piezoelectric materials when shunted to negative capacitance. This paper aims at investigating the effects of negative-capacitance shunt circuits on elastic constants of a piezoelectric ceramic plate through theoretical analyses and experiments, which gives an rational explanation for why negative capacitance shunt circuit is prone to make structure instable. First, the relationships between the elastic constants c₁₁, c₃₃, c₅₅ of the piezoelectric ceramic and the shunt negative capacitance are derived with the piezoelectric constitutive law theoretically. Then, an experimental setup is established to verify the theoretical results through observing the change of elastic constant c₅₅ of the shunted piezoelectric plate with the variation of negative capacitance. The experimental results are in good agreement with the theoretical analyses, which reveals that the instability of the shunt damping system is essentially caused by the singular variation property of the elastic constants of piezoelectric material shunted to negative capacitance.