Axisymmetric Vibrations of a Piezoelectric Spherical Shell Submerged in a Compressible Viscous Fluid Medium

Abstract

Axisymmetric vibrations of a hollow piezoelectric sphere submerged in a compressible viscous fluid medium are investigated. The piezoelectric sphere is radially polarized. The differential equations governing the shell motion are obtained by the use of Hamilton’s principle. Based on the classical bending theory of shells, it is shown that all the piezoelectric contributions can be included in the in vacuo natural frequencies and their corresponding mode shapes. As such, the previous theory on elastic shell vibration becomes readily extendable. The flow field, determined by the boundary layer theory, is coupled to the shell motion through no-slip and no-penetrating conditions. It is found that the contribution of the piezoelectric parameters in the thin shell’s free vibration is of small order and is negligible. Natural frequencies and their associated vibration characteristics are numerically obtained and presented for a Polyvinglindene fluoride (PVDF) shell submerged in water. Dynamic responses of a submerged piezoelectric sherical shell, and the associated radiation of sound are investigated. The oscillations are harmonically driven by an axisymmetrically applied electric potential difference across the surface of the shell. The vibrational, fluid loading, and energy flow characteristics are derived and evaluated for a PVDF shell submerged in water. The essential feature of the modal response is determined by various critical frequencies, such as resonant frequencies and vibration-absorbing frequencies. Viscous effect is found noticeable in several cases.