Modelling and characterisation of shear modes of rectangular piezoelectric materials

Abstract

This article presents a new approach based on an approximate non-standard method for modelling shear modes of piezoelectric ceramics. Coupling between shear modes is introduced by assuming that the electric field inside the element depends on coordinates. Coupling between shear and longitudinal modes is inserted in modelling by using a specific property of partial derivative. Electric field is used in place of the electric density to solve particular dynamic equilibrium equations. Then, the resonance frequency identification of elements having dimensions which do not comply with Standard requirements becomes possible. The element impedance equation includes shear and longitudinal resonance modes. Shear velocity equations calculated with the model are in accordance with those deduced from Standards. New modelling describes the origin of the “aspect ratio” and explains 1D model limitations. Particular resonance conditions of the element are defined. The new model is used for identifying and characterising shear vibration modes of rectangular piezoelectric materials. Shear parameter determination of piezoelectric ceramics is carried out by comparing measured and calculated electric impedance. Measured impedance spectrum displays four resonance peaks which are easily identified using the new modelling. Among these resonances, three are related to shear modes and one to a longitudinal mode which propagates along with poling direction. Coupling between shear and longitudinal modes leads a new EMC Factor. Measured longitudinal displacement validates the proposed modelling.