Response of a multi-layered infinite cylinder to a plane wave excitation by means of transfer matrices

Abstract

A 4×4 transfer matrix is derived to evaluate the response of a multi-layered infinitely long elastic cylinder imbedded in a fluid and enclosing another fluid, to a given one-dimensional pressure excitation, or alternatively to evaluate the acoustic pressure distribution excited by the radial velocity component of the radiating surface. It is shown that the transfer matrix can be effectively used to obtain the scattering coefficient and noise reduction of a multi-layered cylinder for the case of normal incidence of a plane wave. Expressions for several particular cases, such as monostatic back scattering, scattering from a rigid cylinder and a soft cylinder, a solid and a fluid cylinder, are presented. It is shown analytically that the expressions for scattering coefficient for the general case of a hollow cylinder and the particular cases of a fluid cylinder and a solid cylinder lead to the same expressions obtained by using a normal mode solution. Numerical results for the scattering form function and noise reduction of a two-layer infinite cylinder are given to illustrate the effect of layer material characteristics, variation of thickness of either of the constituent layers, cylinder dimensions, and ambient media. Finally, a four-layer hose has been analyzed in order to demonstrate the computational advantage of the transfer matrix method.