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

To gain an understanding of the electroelastic 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 diameterto- 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 toward a finite element model that describes the properties of tactile sensors in detail.