Construction of Shell Theories with Fluid Loading to Approximate Scattering fromSubmerged Bounded Objects via Techniques in a Differential Geometry. (Reannouncement with New Availability Information)

摘要

One can predict sound scattering from fluid loaded elastic shells based on exactelastodynamic theory provided the shell is a sphere or an infinite cylinder or some other geometry for which the elastodynamic equations are separable. Problems arise for more general shapes with only limited success for spheroids and cylinders with hemispherical end caps using the Extended Boundary Condition (EBC) method of Waterman. Both Radlinsky and the Varadans have employed a marriage of the EBC method with shell theories with some progress being made in the description of the scattering event. With this in mind, our objective is to extend the progress made by the above researchers by employing more physical shell theories. It is usual to construct shell theories via use of geometrical constructions, or by use of variational principles. In this study we explore the use of principles from differential geometry to construct appropriate theories that include translational motion and rotary inertia, as well as effects due to fluid loading. Some common thin shell theories which are employed for spherical elastic shells are deduced from these general terms and are compared to exact theory for verification as well as a test of limitations.... Acoustic scattering, Shallow water, Waveguide propagation.