Bulk modulus of a fluid−filled spherical shell
Marshall Hall · The Journal of the Acoustical Society of America · 1975
The zeroth mode of vibration of a fluid−filled elastic spherical shell is examined, and a simple expression is obtained for the bulk modulus of the shell. The expression obtained is a function of the bulk moduli of the fluid and the solid, the shear modulus of the solid, and the ratio of the external and internal radii of the shell. This formula approaches the correct asymptotic values when the internal radius approaches the external radius, and also when the internal radius approaches zero. If the shell is placed in an incompressible medium, it will have a resonance frequency which is determined by the bulk modulus of the shell and the density of the medium. Subject Classification: 40.26.