Sample aspect ratio influence on the shear coefficients measurements of a piezoelectric bar

The variation of the shear related coefficient measurements of a piezoelectric bar with respect to the sample aspect ratio is investigated. This study is carried out with PZT P188 and PZT P189 prismatic rods. The inter-electrodes distance is t and L is the length along the polar axis. Samples with aspect ratio t/L lying between 0.04 and 20 have been characterised using a resonance method. The k₁₅ coefficient is then derived with either a constant field model (high t/L) or a constant induction model (small t/L). The dependencies of k₁₅, d₁₅ and ε₁₁^T on the aspect ratio are given. The derived d₁₅ constants are compared with a direct measurement, made in a quasi-static mode using a Laser Doppler Vibrometry technique, and with ATILA F.E.M. simulations. For low t/L ratios, a clamping of the bar is shown. Moreover, ε ₁₁^T is strongly dependent on the aspect ratio. For high t/L ratios, no clamping is observed and the permittivity is roughly constant. Finally, the use of a constant field model is justified. The best agreement between the different analyses is obtained for t/L ratios higher than 8