Inverse model of the piezoelectric ceramic polarization under wide bandwidth mechanical excitations with fractional derivative consideration

Abstract

This paper presents an inverse piezoelectric ceramic polarization model, $T(P)$, working in wide bandwidth under various mechanical excitations. The model was derived from the polarization model under electric field, $P(E)$, by use of the correlation ($E =\alpha \cdot T\cdot P$) between the external mechanical excitation and piezoelectric ceramic electric field. Using the model, $T(P)$, a given polarization could be obtained by calculating the mechanical stress waveform applied to the ceramic. The piezoelectric ceramic P188 was investigated in the experiment; measurement bench and procedures have been developed to evaluate the accuracy of the model. By means of modeling dynamic counterpart (a fractional derivative part), large range of frequency ($10^{-3} \text{ Hz } < f < 10 \text{ Hz }$) imposed polarization have been examined and experimental results turned out to be good both with sinusoidal and triangular waveforms. The same fractional derivative operator is universal both in mechanical and electrical excitations.