Axisymmetric vibrations of a viscous-fluid-filled piezoelectric spherical shell and the associated radiation of sound

Axisymmetric vibrations of a viscous-fluid-filled piezoelectric sphere, with radial polarization, submerged in a compressible viscous fluid medium are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. A theoretical formulation cast the piezoelectric shell problem into a corresponding problem of an elastic shell with the contribution of piezoelectricity confined to slightly modified in vacuum natural frequencies and their associated mode shapes. It is noted that the fluid inside the shell will have a dominating influence on the vibrational characteristics of the submerged shell. The circular components of the natural frequency spectra closely follow those of the fluid-filled shell in vacuo. Furthermore, the corresponding damping components of those natural frequencies are rather small, making acoustic radiation and under-damped oscillation possible for an infinite number of natural frequencies. The characteristics of natural frequencies are elucidated using a fluid-filled polyvinglindene fluoride (PVDF) shell submerged in both air and water as an example. It is found that the piezoelectric parameters that contribute to the shellʹs natural frequencies is of a small order for thin PVDF shells, and is thereby negligible. It is noted that, with the mechanical constant typically associated with piezoelectric materials, fluid viscosity could have a significant effect on some vibrations. In certain cases, a natural frequency associated with a minimum viscous damping and a maximum of total damping (indicating highly efficient acoustic radiation) is possible with such a frequency. brational characteristics, fluid loading, and energy flow are evaluated for a fluid-filled PVDF shell submerged in air and water. The inclusion of fluid inside the shell is shown to produce various narrow band peaks responses, vibrational absorbing frequencies, and non-dissipating frequencies. Those vibrational characteristics could have many potential applications. For example, the interior fluid could offer the option of generating a desired narrow band near resonant sound radiation while keeping power dissipation due to fluid viscosity to a minimum. Those well-defined narrow band characteristics also open up possibilities of using a vibrating, fluid-filled shell as a micro scale sensor for sensing and detection applications.