A Model of an Infinite Length, Axisymmetric, Isotropic, Forced Thick Shell
NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV NEW LONDON CT NEW LONDON DETACHMENT
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The model described in this report provides an exact solution to the equations of motion for an infinite length, axisymmetric, isotropic, forced thick shell. In this model, the governing equations of motion of an isotropic elastic solid in cylindrical coordinates are first separated into a dilatational wave equation and three distortional wave equations that can be solved with Bessel functions. These general solutions are then inserted into stress-strain constitutive equations at the interior and exterior of the shell. The displacements are next determined from forcing functions that are applied to the shell. In this new model, the shell thickness effects on wave propagation are addressed. The case where the mean radius of the shell is equal to its thickness has been analyzed and compared with thin shell equations of motion. It is shown that, in general, the thin shell equations of motion often underpredict thick shell response.
- Numerical Mathematics