Some aspects of wave propagation in thin elastic shells are considered.The governing equations are derived by a method which makes theirrelationship to the exact equations of linear elasticity quite clear.Finite wave propagation speeds are ensured by the inclusion of the appropriatephysical effects.
The problem of a constant pressure front moving with constantvelocity along a semi-infinite circular cylindrical shell is studied. Thebehavior of the solution immediately under the leading wave is found, aswell as the short time solution behind the characteristic wavefronts. Themain long time disturbance is found to travel with the velocity of verylong longitudinal waves in a bar and an expression for this part of thesolution is given.
When a constant moment is applied to the lip of an open sphericalshell, there is an interesting effect due to the focusing of the waves.This phenomenon is studied and an expression is derived for the wavefrontbehavior for the first passage of the leading wave and its first reflection.
For the two problems mentioned, the method used involves reducingthe governing partial differential equations to ordinary differential equationsby means of a Laplace transform in time. The information sought isthen extracted by doing the appropriate asymptotic expansion with the Laplacevariable as parameter.
