Investigation of vibrations of piezoelectric spherical shells with axisymmetric holes

Abstract

An experimental investigation of the vibration of radially polarized thin-walled piezoelectric ceramic spherical shells with axisymmetric holes is presented. Piezoelectric spherical electroacoustic transducers having holes at their poles to permit passage of wires, cables, or structural members is of particular interest in underwater acoustics. The coupled vibrations follow three resonance branches corresponding to (0) azimuthal extensional modes, (1) bending flexural modes, and (2) meridional extensional modes. The resonances and effective electromechanical coupling coefficient for each mode as a function of the hole-to-sphere diameter ratio have been determined from admittance measurements. In the limit that the hole-to-sphere diameter ratio approaches zero, the (0) mode is dominant corresponding to the spherically symmetric breathing mode having a measured coupling coefficient of 0.546, which is consistent with the planar coupling coefficient for PZT-4 (Type I) material. In the limit that ratio approaches unity, the element in nearly cylindrical and the lowest (0) mode corresponds to the breathing mode of a ring having a coupling coefficient of about 0.33, which is consistent with the transverse (31) coupling coefficient for the material. The focus of the study is on determining the resonances and electromechanical coupling in the intermediate region and obtaining corresponding vibration mode shapes with a non-contact optical fiber displacement sensor.