Improved calculations of the electromechanical properties of tangentially poled stripe-electroded piezoelectric bars and cylinders with nonuniform electric fields^a)

Tangentially polarized stripe-electroded piezoelectric elements are often used to achieve the longitudinal piezoelectric effect without using segmented parts bonded together, however the electromechanical properties are not fully realized due to the nonuniform electric field and polarization in the element. The effective electromechanical coupling coefficient k_3′3eff, piezoelectric modulus d_3′3eff, elastic constant $s3'3effE$⁠, and relative dielectric constant $ε3'3effT$ (where the prime denotes the nonuniform polarization) for tangentially polarized stripe-electroded bars and hollow cylinders are calculated using the energy method for the nonuniform electric field. A finite difference method is used to analyze the electric field under the assumption that the piezoelement is fully polarized. Results are compared with a piecewise linear field model and experimental results on representative piezoelements.