Study on frequency dependence of polarized piezoceramics constants in equivalent circuits at weak electric fields (part III)

Introduction. It is acknowledged that electroelastic modules do not depend on the amplitude and frequency of oscillations. This approach is reflected in the Russian and foreign standards for determining the complete set of electro-elastic piezoceramics modules. For example, to determine d₃₁ piezomodule of a disc-shaped sample, it is required to take measurements in three frequency domains: in the first and second resonances, in the antiresonance region, and at frequencies much below 1 kHz. Accordingly, it is assumed that when determining d₃₁, the modules of the ceramic under study in the frequency range from 1 KHz to the second resonance are independent of frequency. The work objective is to study the frequency dependence of electro-elastic ceramic modules. In this case, a disc-shaped sample from LZT (lead zirconate titanate) is used.

Materials and Methods. Techniques of setting and solving problems of the stationary electroelasticity and sections of the electrical engineering basics are applied. To implement the finite element method, the perturbation technique and the ANSYS application package are used. The experimental results are processed in the MATLAB environment.

Research Results. For the LZT piezoelectric ceramics, the frequency dependences of various modules (piezoelectric d₃₁, dielectric ε₃₃^???????? and elastic modules of compliance ????????₁₁, ????????₁₂, ????????₁₃) were investigated. Radial oscillations of a discshaped sample with electrodes on the ends were considered. The sample thickness was 1 mm, the diameter was 40 mm, and the oscillation range was up to 700 KHz. First, the frequency dependence was studied for the elastic ceramic modules from the determination of ten resonance frequencies. Then, the frequency dependence of d₃₁and ε₃₃^???????? modules was determined from the measured values of the sample conductivity. For this purpose, we used the expression for the electrical conductivity obtained from the solution of the radial oscillations of the disc considering its thickness.

Discussion and Conclusions. A technique is developed for determining the frequency dependence of LZT piezoelectric ceramic modules. The disc-shaped sample was studied in 15650 KHz frequency range. It is shown that in the range up to 650 KHz, ????????₁₁, ????????₁₂, ????????₁₃ elastic modules with E superscript (it is omitted) or measured at dc field are practically independent of frequency. In the specified range, ε₃₃^????????, d₃₁, kp constants have an insignificant frequency dependence for the considered radial oscillations.

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