Experimental investigation of coupled vibrations in piezoelectric cylindrical shells

An experimental investigation of the electromechanical properties of radially polarized thin-walled piezoelectric ceramic cylinders as a function of the height-to-diameter aspect ratio is presented. The focus of this investigation is on the lowest order axially symmetric modes of vibration for cylinders with free ends having aspect ratio less than 3 with emphasis on the region of strongest coupling around aspect ratio π∕2. The resonance frequencies and coupling coefficients are presented vs aspect ratio and quantify the lower, upper, and an intermediate resonance branch. It is shown that the intermediate branch is flexural in origin and clearly crosses the so-called “dead zone,” which is an inadequacy of the membrane theory applied to the vibration of thin shells [Junger and Rosato, J. Acoust. Soc. Am., 26, 709–713 (1954)]. The coupling coefficient for the lower branch is shown to drop to zero at h∕2a=π∕2, whereas the coupling coefficient associated with the upper branch reaches a maximum at an aspect ratio near this region. As an example of the practical application of this study, the performance of two underwater electroacoustic transducers comprised of cylindrical elements having different aspect ratios is reported.