Radiation and radiation impedance on fluid-loaded elastic shells of arbitrary shape

摘要

A ray method is systematically used to derive a relation between radiated acoustic waves and elastic waves traveling over a smooth elastic shell of arbitrary shape. The radiated acoustic field is found to be intimately connected with the geometries of the shell's surface and the elastic wavefronts. This connection leads to an asymptotic expression for the local radiation impedance associated with each surface ray under the condition k_fR > > 1, where k_f is the wavenumber in fluid and R the smallest radius of curvature of the shell. The first term in this formula is the result for an infinite flat plate, which is homogeneous and isotropic. The second term introduces inhomogeneity and anisotropy into the radiation impedance because it explicitly depends on the surface ray direction and the local curvatures of the shell's surface and the elastic wavefront. The general result is further simplified for a cylindrical shell of arbitrary smooth cross-section. The comparisons with the exact solutions for circular cylindrical and spherical shells illustrate that the present results can reproduce the first two terms in the asymptotic expansions of the exact solutions.