Mode Identification In Resonant Ultrasonic Spectroscopy Technique For The Determination Of Full Set Material Constants Of Piezoelectric Materials

Piezoelectric materials,as important functional materials,have been applied in many fields where piezoelectric materials are used as core materials.The premise of designing piezoelectric devices is that they have an accurate measurement of piezoelectric materials constants.The material constants can be inversed from the ultrasonic resonance spectrum by measuring the resonant frequency of the sample.However,this process requires accurate identification of the resonant peaks.According to the measured frequency range of the ultrasonic resonance spectrum,the number of resonance peaks ranging from dozens to hundreds.How to accurately identify the resonant modes of the resonant peaks in the ultrasonic resonance spectrum so that the material constants could be correctly inversed is the main concern of this dissertation.In this dissertation,the ultrasonic resonance spectra of the isotropic ceramics(unpoled PZT8 ceramics)and anisotropic piezoelectric single crystals were measured and studied,and the accurate identification of the important resonance modes of the ultrasonic resonance spectra is realized,which make the correct inversion of the material constants of the piezoelectric materials possible.With given material constants,the resonant frequency of the material could be calculated by using the Lagrangian variational method and finite element calculation software.The influence of the order of the basis functions on the calculation accuracy is studied.At the same time,according to the symmetry of the crystal,the resonance modes are classified,which lays a foundation for pattern recognition.The influence of specific constants on each resonant frequency was studied in order to find out those resonnant modes which are sensitive to the specific constants.The elastic matrix of the unpolarized PZT8 ceramic material and the full-matrix parameters of the PZN-5.5%PT single crystal were obtained by solving the nonlinear least-squares problems.A mode recongnition method is proposed in the dissertation by analyzing the parity of the displacement function and the parity of Legendre polynomials.That is,the parity of the Legendre polynomial determines the displacement distribution characteristics of the sample surface.Thus,the resonance mode of the sample at the resonnant frequency can be determined by studing the displacement distribution,which lays a foundation for the inversion calculation mode matching.The mode recognition methods and procedures,as well as the inversion of elastic matrix and full-matrix constants,given in this dissertation can be applied not only to piezoelectric materials but also to other materials with low loss factors.