Modeling and characterization of thick piezoelectric disk including radial, longitudinal and shear modes

Abstract

The article deals with the complete modeling and characterization of thick piezoelectric ceramics. Modeling is based on radial and longitudinal mode determination of a thick piezoelectric disk. Shear modes are inserted in the modeling using the properties of partial derivatives. Displacements calculation of the three vibration modes leads to the determination of the general impedance of a thick disk. Modeling leads to new electromechanical coupling factors (EMC factors) showing the influence of coupling between: longitudinal-radial, longitudinal-shear and also shear-longitudinal modes. Using one-dimension hypotheses, longitudinal and radial 3D-EMC factors reduce to the well-known EMC factors defined by Standards. EMC factors related to coupling between longitudinal and shear modes are new. Complete characterization of the piezoelectric ceramic disk has been carried out for calculating all the constant-E and constant-D elastic constant (2 × 6) and the three piezoelectric coefficients related to the disk. Calculated elastic constant matrix is consistent because it does not depend on compliances.