The radiation of sound from a finite ring-forced cylindrical elastic shell I. Wiener–Hopf analysis

Abstract

The radiation of sound from a finite fluid-loaded cylindrical elastic shell is examined by means of the modified Wiener–Hopf technique. The shell is freely submerged in an inviscid compressible stationary fluid of infinite extent and axisymmetrically excited by a ring force. The problem is formulated as a three-part Wiener–Hopf equation with three unknown functions, and is recast as two uncoupled Fredholm integral equations of the second kind by utilizing a factorization and decomposition procedure. When the product of the cylinder length l and the wave number k is large, asymptotic analysis can be applied to the integral equations, which reduces them to a finite system of algebraic equations corresponding to a set of unknown constants, including the edge displacements. The method provides a straightforward formulation for the solution and is valid for arbitrary fluid loading. Numerical results are presented for the radiated far-field velocity potential. This requires a numerical decomposition of the Wiener–Hopf kernel and the solution of the set of simultaneous equations.