A FEM-based method using harmonic overtones to determine the effective elastic, dielectric, and piezoelectric parameters of freely vibrating thick piezoelectric disks

Abstract

To gain an understanding of the electro-elastic properties of tactile piezoelectric sensors used in the characterization of soft tissue, the frequency-dependent electric impedance response of thick piezoelectric disks has been calculated using finite element modeling. To fit the calculated to the measured response, a new method was developed using harmonic overtones for tuning of the calculated effective elastic, piezoelectric, and dielectric parameters. To validate the results, the impedance responses of 10 piezoelectric disks with diameter to thickness ratios of 20, 6, and 2 have been measured from 10 kHz to 5 MHz. A two-dimensional, general purpose finite element partial differential equation solver with adaptive meshing capability run in the frequency-stepped mode, was used. The equations and boundary conditions used by the solver are presented. Calculated and measured impedance responses are presented, and resonance frequencies have been compared in detail. The comparison shows excellent agreement, with average relative differences in frequency of 0.27%, 0.19%, and 0.54% for the samples with diameter to thickness ratios of 20, 6, and 2, respectively. The method of tuning the effective elastic, piezoelectric and dielectric parameters is an important step towards a finite element model that describes the properties of tactile sensors in detail.

Modeling the high-frequency complex modulus of silicone rubber using standing lamb waves and an inverse finite element method

“…The finite element equations and boundary conditions presented in this section form an extension of the finite element partial equations solver model (Psm) [14]. The extension handles losses in the sensor and models the viscoelastic properties of the srd.…”

“…The following parameters described the vibrational characteristics of the sensor: the elastic parameters c 11 , c 12 , c 13 , c 33 , and c 44 ; the piezoelectric parameters e 31 , e 15 , and e 33 ; the dielectric parameters ε 11 and ε 33 ; and the loss tangent, η. because the sensor was identical to a piezoelectric element (PZT-5a1, morgan Electro ceramics, Thornhill, southampton, England) that was modeled in an earlier work, the Pd02 model [14], the parameters were identical to the effective Pd02 model parameters with the addition of the loss tangent parameter.…”

“…The elements of the matrix are the ratios of the relative variation of target frequency-thicknesses to the relative variation in parameter values [14]. The parameters were tuned using the feedback algorithm for the determination of grouped parameters [14], here called the parameter tuning procedure (PTP).…”

“…To match the baseline of the Psm model to the measured baseline, the elastic parameters c 11 , c 12 , and c 13 of the sensor were used. They are dominant in the lowfrequency tuning stage sensitivity matrix [14] for the R 1 and R a 1 radial resonances. The parameters were tuned using the PTP.…”

“…The creation of a FEm model of the tactile sensor-tissue system and fitting the model to measurements of the vibrational spectra will be an important step toward a deeper understanding of the interaction between the vibrating sensor and the soft tissue with which it is in contact. In the process of creating such a FEm model, as a first step, cylindrical piezoelectric elements have been characterized using a FEm model utilizing harmonic overtones [14].…”