Inverse Evaluation of Material Constants for Piezoceramics by Out-of-Plane Vibration

Abstract

A full-field optical technique called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), together with out-of-plane measurement, is employed to investigate the vibration characteristics of completely free piezoceramic rectangular plates. Because the interferometric fringe patterns will be presented clearly only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained by AF-ESPI at the same time. With the experimental results from the first few out-of-plane vibration modes, an inverse evaluation for the material compliance constants of piezoceramics is developed using the Rayleigh-Ritz method incorporated with the Simplex algorithm. As compared to the traditional method using radial in-plane modes of piezoceramic disks, the transverse resonant frequencies of rectangular plates are employed for the proposed methodology. Finite element method calculations are also performed to construct the mode shapes from the obtained material constants by inverse evaluation, and the results are compared with the experimental observations. This experimental method based on an optical AF-ESPI setup and the inverse algorithms proposed might become a reliable and self-consistent methodology for evaluating material constants of piezoceramic plates. NomenclatureA = amplitude of out-of-plane vibration A = amplitude of in-plane vibration c E i jkl , c E pq = elastic constant at constant electrical field D i = electrical displacement component D i j = bending stiffness d kp = piezoelectric constant E k = electrical field component e ki j , e kp = piezoelectric constant h = plate thickness I O = object light intensity I R = reference light intensity J 0 = zero-order Bessel function of first kind J 1 = first-order Bessel function of first kind S i j , S p = strain component s E pq = compliance constant at constant electrical field T i j , T p = stress component t = time u j = mechanical displacement field x, y, z = Cartesian coordinate system ε S ik = dielectric constant at constant strain ε T ik = dielectric constant at constant stress λ = wavelength of laser ρ = material density τ= charge-coupled device refreshing time = phase difference between reference and object lights = phase difference between two object lights = angle between object light and observation direction = one-half of angle between two object lights ω = angular frequency