Electromechanical coupling coefficient of an ultrasonic array element

One of the most important parameters for characterizing piezoelectric materials is the so-called electromechanical coupling coefficient, k, which describes the electromechanical coupling strength. Although this parameter should be an intrinsic material parameter, it appears to depend on the aspect ratio of the resonator. There are three different values defined for three extreme geometries, k33, k33′, and kt, and they differ by more than 50%. Unfortunately, these three values cannot describe resonators of general geometries and also create conceptual confusion. Here, we provide a unified formula that will accurately describe the coupling coefficient of rectangular slender bar transducer array element with any aspect ratio.