Analysis of methods for determining electromechanical coupling coefficients of piezoelectric elements

An important characteristic of piezoelectric elements as energy converters is the energy conversion efficiency. The electromechanical coupling coefficient (EMCC) is commonly used as a measure of a piezoelectric elements´ efficiency. The latest Standard on Piezoelectric recommends that EMCC be determined by the use of the Berlincourt et al. formula for a uniform electroelastic state, and the dynamic formula by Mason for near resonance frequencies. This paper is devoted to the analysis of these two formulas along with a third formula. The EMCC of commonly seen piezoelectric elements are formulated and analyzed. The comparison of the numerical results leads us to the following conclusions: 1. The formula of Berlincourt et al. is valid only for a uniform electroelastic state, 2. The dynamic formula of Mason gives the EMCC at a frequency equal to the arithmetic mean of resonance and the corresponding antiresonance frequencies, 3. The third formula for the EMCC is valid for both the static and dynamic electroelastic state of a piezoelement, and its results are in good agreement with those found by using Berlincourt´s formula and the dynamic formula of Mason.<>