A Mathematical Model for Polarization Dynamics in a BTS 15 Ceramics

Abstract

In this paper, a ferroelectric structure consisting of barium stannate titanate piezoelectric ceramic is used for mathematical modeling. The study of the dynamics of the structure requires the poling process that makes the ceramic active. This may be explained by the time-dependent nonlinear polarization behavior. The model results in a nonlinear second order ordinary differential equation of one degree of freedom. Analytical exact solutions have been obtained for three regimes following the specific value of the damping parameter. Numerical simulations of these solutions by optimization with Matlab package showed excellent agreement in comparison with measurements and a mean square error of order of 10-5 is obtained.