Electronically tunable auxetic behavior of shunted piezoelectric elements

Abstract

This work demonstrates auxetic behavior in a solid polycrystalline shunted piezoelectric cube. Piezoelectric elements are commonly bonded to structures to reduce vibrations by tuning an attached shunt circuit to resonate at the same frequency as the mechanical vibrations in the structure. Literature has provided an extensive analysis of vibration suppression in passively shunted piezoelectric systems, but in practice, the three-dimensional constitutive equations are almost always reduced to one-dimensional stresses and strains within the piezoelectric. In this work, resistive–inductive shunt circuits are applied to the electrical terminals of a harmonically forced piezoelectric cube, and the directional displacements are determined in all three dimensions when it is loaded parallel and perpendicular to the poling direction, as well as dilatationally. By comparing these directional displacements, the effect of the shunt circuit on Poisson’s ratio can be measured. It is demonstrated that an inductive shunt leads to a complex Poisson’s ratio with a real part approaching positive and negative infinity over a discrete band of frequencies, implying that a polycrystalline piezoelectric cube can become auxetic through the application of a properly engineered shunt circuit. The auxetic behavior is explored through finite element modeling, and the derivation of analytical expressions for Poisson’s ratio in shunted piezoelectric elements.