Resonance modes in the standard piezoceramic shear geometry: A discussion based on finite element analysis

Abstract

Abstract. Several authors developed methods for the complex characterization of piezoceramics from complex impedance measurements at resonance. Alemany et al. developed an automatic iterative method, applied and reported in a first publication to four modes of resonance: (1) the length extensional mode of a thickness poled rectangular bar; (2) the length extensional mode of long rods or rectangular bars, length poled; (3) the thickness extensional mode of a thin plate and (4) the thickness shear mode of a thin plate. In a second publication it was reported the application of the method to (5) the radial mode of a thin disk, thickness poled, the most mathematically complex geometry. The (2), (3), (4) and (5) modes of resonance are sufficient for the purpose of the determination of the full set of complex elastic, dielectric and piezoelectric coefficients of piezoceramics, a 6mm symmetry material. This work presents the results of the FEA modeling of a thin plate based on the characterization of a commercial ceramic. The comparison of the experimental resonance spectra and the FEA results obtained for elastically, dielectrically and piezoelectrically homogeneous samples is presented and discussed. The complex characterization for the first time of the shear mode of a new lead-free piezoceramic is also shown.

Study by laser interferometry of the resonance modes of the shear plate used in the standards characterization of piezoceramics

“…Based on the full characterization mentioned above, FEA modeling has been used to test the validity of the matrix of coefficients obtained by Alemany et al method by reproduction of the measured spectra of the samples used in the characterization [7]. FEA also allows to understand the modes of vibration of the ceramic resonators involved in such characterization, in particular the Standard shear plate [8]. Such type of study aims to optimize the resonator samples, thus improving the method for material characterization and getting more accurate material properties.…”

Key issues in the characterization of porous PZT based ceramics with morphotropic phase boundary composition

“…Besides, recent work of some of the authors [15] has shown that the use of the Standard shear sample (Fig. 1), leads to underestimation of the shear coefficients which, according to results of the modeling of the resonances of this sample by FEA, is due to a dynamical clamping of the sample.…”

“…This fact, coupled to the dynamical clamping of the Standard [15], severely limits the application of the solution obtained by the Alemany et al method in the matrix characterization. As an example, data in Table 4 show that all elastic losses, as revealed by the imaginary part of the elastic coefficients, determined from the Standard sample are much higher than those determined for the non-standard one.…”

Choosing the best geometries for the linear characterization of lossy piezoceramics: Study of the thickness-poled shear plate

“…The dynamic clamping at resonance of the Standard plate, which leads to underestimation of the piezoelectric coefficients of the ceramics, was recently discussed. 5,6 Porous ceramics 7 are an example of materials in which the Standard plate cannot be used for characterization due to the added problem of difficult poling in the long dimension of the sample.…”

“…These electrodes were removed and new ones were attached at the perpendicular surfaces for the electrical measurements in a HP4192A low frequency impedance analyzer and the laser interferometric measurements, as explained elsewhere. 5 Conductance ͑G͒ and resistance ͑R͒ peaks derived from the complex impedance measurements of the fundamental shear resonance of the three samples are shown in Fig. 1.…”