Modelling of coupling between shear and longitudinal modes of a bulky rectangular piezoelectric element

Abstract

This article presents a new approach based on an approximate non-standard method for modelling shear modes of rectangular piezoelectric ceramics. Coupling between shear modes is introduced by assuming that the electric field inside the element depends upon coordinates and by using a specific property of partial derivative. Electric field is used in place of the electric density to solve the dynamic equilibrium equations and particular resonance conditions of the element are defined. Then, the resonance frequency mode 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 phenomenon’ and explains 1D-model limitations. 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 correctly identified using the new model. Among these resonances three are related to shear modes and one to a longitudinal mode which propagates along with poling direction. The new modelling leads to a new EMC Factor which clearly shows the origin of coupling between shear and longitudinal modes. Measured longitudinal displacement validate the proposed modelling.