Transient response of two fluid-coupled spherical elastic shells to an incident pressure pulse

The transient response of a system of two initially concentric spherical elastic shells coupled by an ideal fluid and impinged upon by an incident plane pressure pulse is analyzed. The classical techniques of separation of variables and Laplace transforms are employed for solving the wave equations governing the fluid motions and the shell equations of motion. A scheme of iterative convolution was devised for the inversion of the Laplace transforms that facilitates the calculation of accurate transient solutions of the response of the shells. A sample calculation of shell responses was performed and results are compared to the case in which the outer shell is absent. This set of results demonstrates that a thin outer shell tends to be transparent to the incident pulse.

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