Nonspecular reflection of two- and three-dimensional acoustic beams from fluid-immersed cylindrically layered elastic structures

Abstract

This paper extends the complex ray analysis developed for nonspecular reflection of quasi-Gaussian acoustic beams from fluid-loaded plane elastic structures [S. Zeroug and L. B. Felsen, ‘‘Nonspecular reflection of two- and three-dimensional acoustic beams from fluid-immersed plane layered elastic structures,’’ J. Acoust. Soc. Am. 95, 3075–3089 (1994)] to cylindrically layered configurations. Except for the adaptation to cylindrical geometry, the rigorous spectral and subsequent asymptotic techniques employed for the plane layered case remain intact. Thus the quasi-Gaussian beams with arbitrary collimation and arbitrary incidence angles are again modeled by the complex source point (CSP) method and the formal complex wave-number spectral integrals for the total scattered field are reduced asymptotically to yield numerically efficient algorithms parametrized in terms of self-consistently interacting specularly reflected and leaky wave fields, which model the proper wave physics. Results are obtained for reflection of two-dimensional (2-D) and three-dimensional (3-D) CSP beams from an aluminum solid cylinder in water, and for 2-D CSP beams from a fluid-loaded cylindrical shell whose modes are assumed, in the high-frequency regime, to be derivable approximately from those for the fluid-loaded plate. The data reveal a strong dependence on the cylindrical surface curvature which manifests itself in the resulting reflectivity pattern through multiple beam splitting for diverging as well as collimated incident beams. These observations pertain not only when the incident beam is phase matched to a leaky wave but also for incidence angles far from the phase-matched condition. Physical explanations are given for these phenomena which are compared with, and related to, those encountered for the planar configurations. As for the planar case, the outcome is a versatile algorithm for predicting interaction of arbitrarily collimated 2-D and rotationally symmetric 3-D acoustic beams with cylindrically curved elastic media, at arbitrary angles of incidence.