Phil. Trans. R. Soc. A (2011) 369, 2852–2863 doi:10.1098/rsta.2011.0098 Sound scattering by free surface piercing and fluid-loaded cylindrical shells BY ELDAD J. AVITAL 1 AND TOUVIA MILOH 2, * 1 School of Engineering and Materials, Queen Mary University of London, London E1 4NS, UK 2 Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel A vertical flexible, thin, cylindrical shell is considered to be clamped to a rigid base in shallow water and piercing its surface. The shell is composed of an isotropic and homogeneous material and may be empty inside or filled with compressible fluid. Linear acoustics and structural dynamics are used to model sound scattering caused by an external incident sound wave. A solution is derived using a Fourier transform in the tangential and vertical directions. A collocation technique coupled with an orthogonalization procedure is used to account for the edge conditions of the shell. It is shown that zero sound scattering, indicating acoustic invisibility, is theoretically attainable and can be achieved when a continuous distribution of an oscillating pressure load is applied on the shell’s wall. Similarly, zero sound transmission into the shell’s inner fluid can also be considered. The possibility of using a pre-determined discrete distribution of the applied pressure load is also discussed. The derived equations are numerically solved to examine sound scattering by a thin aluminium shell in shallow water. Keywords: general linear acoustics; structural acoustics and vibration; underwater sound 1. Introduction This paper deals with the interaction between a flexible vertical cylindrical shell piercing a free surface and an externally generated sound field. Attention is directed towards the potential offered by the flexibility of the shell to reduce the scattering of sound caused by that interaction. The thin cylindrical shell is a structure of engineering interest across a vast variety of fields ranging from aeronautical to marine applications, such as modelling aircraft fuselages or underwater vessel hulls and offshore structures. Considerable research has been carried out on the interaction between fluid flow and a cylinder piercing the free surface (e.g. [1]). The interaction between an externally or internally generated sound field and a cylinder is also of importance owing to structural considerations, i.e. acoustic pressure loading, comfort for the crew inside the vehicle hull (modelled as a cylindrical shell) and detection purposes. The following paragraphs summarize some of the recent research on this subject. *Author for correspondence (miloh@eng.tau.ac.il). One contribution of 13 to a Theme Issue ‘The mathematical challenges and modelling of hydroelasticity’. This journal is © 2011 The Royal Society 2852 Downloaded from https://royalsocietypublishing.org/ on 21 February 2022