The transient response of a system of two initially concentric circular cylindrical elastic shells coupled by an ideal fluid and impinged upon by an incident plane pressure pulse is studied. The classical techniques of separation of variable and Laplace transforms are employed for simultaneously solving the wave equations governing the fluid motions and the shell equations of motion. The transformed solutions are arranged in such a manner that their inverse transforms can be accurately calculated by solving a set of Volterra integral equations in the time domain. A sample calculation of shell responses was performed and results are compared to the case in which the outer shell is absent. It is found that the primary effects of a thin outer shell could be estimated by simple asymptotic formulas.

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