Axisymmetric Vibration of an Elastic Spherical Shell Filled with a Viscous Incompressible Fluid.
CASE WESTERN RESERVE UNIV CLEVELAND OHIO DIV OF FLUID THERMAL AND AEROSPACE SCIENCES
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The present analysis of a vibrating shell filled with fluid agrees with previous results in the limits of thin shells and zero viscosity, but extends those results to arbitrary shell thickness and viscosity, and obtains the complete frequency spectrum, without the truncation resulting from the assumptions of thin-shell theory. Allowance is made for an arbitrary spherically symmetric static stress distribution, and gravity is taken into account, in view of applications to planetary vibration. The solution is obtained for arbitrary Poisson ratio, and a boundary layer effect is demonstrated in the case of small viscosity. The effect of a fluid center upon lunar vibration is examined, as well as the importance of the hydrostatic assumption for the static stress field. The effect of viscosity is exhibited for a vibrating system comparable to the human eye. Author