Transient Interaction of an Acoustic Wave with a Circular Cylindrical Elastic Shell

Abstract

An infinitely long, circular cylindrical elastic shell is surrounded by an acoustic fluid. A plane pressure pulse, whose front is parallel to the axis of the shell, moves through the fluid, strikes the shell, and subsequently engulfs the shell. The circular shell is replaced by a fictitious Riemann surface which effectively allows the range of θ (the angular coordinate) to be extended from − ∞ to + ∞. Exact expressions are then found for the subsequent shell and fluid motion in the form of double integrals by the use of integral transform techniques. These integrals are evaluated asymptotically by the method of steepest descent to determine the early time motion of the shell and fluid. In particular, it is found that during this early motion the radial shell velocity and bending moment have a maximum, and the fluid pressure at the interface experiences a minimum.