Acoustic Radiation from a Finite Length Cylindrical Shell Excited by an Internal Acoustic Source: Solution Based on a Boundary Element Method and a Matched Asymptotic Expansion

Abstract

This paper deals with acoustic radiation by a thin elastic shell, closed by two perfectly rigid discs, immersed in water and filled with air. The system is driven by an internal acoustic source. The shell has a length L, is clamped along one of its boundaries and is freely supported along the other boundary.

Using the infinite domain Green's function, the radiated acoustic pressure is modeled by a hybrid layer potential (linear combination with nonreal coefficient of a simple layer and a double layer). Using Green's tensor of the in vacuo shell operator, the shell displacement is expressed as the sum of the field generated by the acoustic pressures and that due to boundary sources. Finally, the Green's function of the interior Neumann problem is used to express the acoustic pressure inside the shell in terms of the acoustic source and shell normal displacement: this representation fails for any frequency equal to one of the resonance frequencies of the shell interior.

To overcome this, a light fluid approximation, which is allowed because the inner fluid is a gas, is adopted. Around each resonance frequency, an inner approximation is defined which matches the classical outer approximation.