The most important parameter characterizing a piezoelectric material is the electromechanical coupling coefficient, which specifies the conversion efficiency between electrical and mechanical energies for a given vibration mode. For the resonance along the poling direction, there are two coupling coefficients defined, i.e., kt and k33, which are for resonators of the same mode but two extreme aspect ratios and they differ substantially. We have derived a unified formula for this coupling coefficient as a function of the vibrator aspect ratio. The unified formula can provide more accurate description to the effective coupling coefficient of resonators not satisfying the extreme aspect ratio requirements.
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, k 33 , k 33 Ј , and k t , 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.
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