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Based on ray concepts, a geometrical theory is developed for the analysis and synthesis of the pressure and velocity fields of source‐excited smooth thin elastic shells with fluid loading. At mid frequencies, these fields are contributed mainly by shell guided leaky membrane waves and specular reflection, provided either the source or observer is away from the shell surface. The theory involves the ray divergence coefficients characterizing the evolution of ray tubes in the fluid or ray strips on the shell, as well as the excitation, radiation, and reflection coefficients, which depend on both the physical and the geometrical properties of the shell. The former may be found by geometrical considerations, while the latter are determined by comparison with the analytic solutions of appropriate canonical problems and subsequent generalization to the perturbed shell configurations. Utilizing circular cylindrical and spherical shells as the canonical examples, this paper demonstrates the construction of the scattered fields from cylindrical shells of arbitrary cross section and from shells of revolution. It extends the concepts of Keller and Karal’s geometrical theory for surface waves [J. B. Keller and F. C. Karal, Jr., J. Appl. Phys. 31, 1039–1046 (1960)].

Combining the available ray acoustic algorithms descriptive of submerged cylindrical and spherical shells, this paper formulates the pressure and velocity distributions on a hemispherically capped cylindrical shell which is immersed in an acoustic fluid and insonified by an obliquely incident plane wave. As the first ray acoustic model for a noncanonical (nonseparable) shell geometry of considerable current interest, it neglects wave coupling and diffraction due to curvature discontinuities at the junctures as well as contributions from the leaky waves excited through the endcaps. Nevertheless, by matching the surface wave vectors along the joints, due account is taken of leaky wave propagation on, and radiation from, the hemispheres. The total pressure or velocity on the cylinder—their ray constituents are related to each other by appropriate impedances—is then synthesized by a modified geometrical acoustics field, as developed recently, and a supersonic membrane wave field. The latter is contributed by ...

The presence of conspicuous penumbra regions in near‐field wave scattering renders asymptotic treatment of ray integrals—by Fock’s theory, for instance—extremely involved, especially for elastic shell–fluid boundary conditions. A modified ray acoustic model that avoids these intricacies as well as those associated with reflected‐leaky wave transition regions has recently been proposed, and proved very accurate at moderate and high frequencies for the thin cylindrical shell prototype [J. M. Ho, J. Acoust. Soc. Am. 96, 515–524 (1994)]. Following this approach, this paper discusses the ray synthesis of the on‐ and off‐surface acoustic response of a submerged empty thin spherical shell insonified by an acoustic plane wave. In particular, the two spectral integrals that would yield the incident and reflected ray fields by saddle point reductions are combined into a single integral representing the modified geometrical acoustics field, which may be so rearranged that it is merely the continuum form of the discr...

The near‐field scattering of plane waves by a submerged thin elastic cylindrical shell witnesses a shadow boundary generated by the geometrical acoustics field, which is not encountered in the far field except in the immediate vicinity of the forward scattering direction. Even in the lit zone, the incident and reflected rays may appear close and are not well separated. Based on these physical observations a modified ray acoustic approach is proposed here that combines the two spectral integrals that would give rise to separate incident and reflected fields when reduced by saddle point evaluation. The resulting single integral descriptive of the geometrical acoustics field can be cast as an integral version of the harmonic series form for the total (incident plus scattered) field, thereby facilitating its numerical computation. Averting the asymptotic integration procedure, and hence the contour deformation involving possible capture of the membrane wave poles, the new algorithm predicts the total near fie...

This paper applies uniform ray asymptotics to plane‐wave far‐field scattering by submerged thin elastic spherical shells based on an earlier study [J. M. Ho and L. B. Felsen, J. Acoust. Soc. Am. 88, 2389–2414 (1990)]. It also performs numerical implementation to clarify the ray synthesis accuracy and to examine the constituent waves and fields. Specifically, in addition to the frequency response, the scattering pattern is also evaluated which demonstrates the connection between bistatic (regular) and backscattering (axial focusing). It is found that the major contribution to the total scattered field is from specular reflection, a supersonic compressional wave, and their interaction effect when adjacent, plus a creeping wave field in the forward scattering range—much the same as with the cylindrical shell prototype [J. M. Ho, J. Acoust. Soc. Am. 94, 2936–2946 (1993)], save from the spherical focusing of the shell‐guided waves here. These wave objects together reproduce the scattering signature, as generated by the exact normal‐mode series solution, very accurately for ka≥5 or so.

In a uniform ray acoustic formulation, the pressure field scattered by a submerged thin elastic cylindrical shell is comprised of a specular reflected wave field, a phase‐matched leaky wave field, and a reflected–leaky wave interacting field. They correspond to the contribution from a saddle point, the residue from spectral poles, and the effect due to their proximity in the spectral ray integral generating the reflected field. Using plane wave far‐field scattering as an example, this paper presents an improved uniform algorithm that expresses the third component in terms of the first and second, which have been developed earlier, plus a complementary error function. In addition, the creeping wave contribution is also considered. Numerical implementation is carried out, showing extensively the scattered field data, in particular, their dependence on frequency as well as on aspect and azimuthal angles; the ray constituents and interacting fields are identified individually, thereby clarifying the relevant ...

An important step in dealing with the mass‐spring loaded cylindrical shell is to evaluate the total shell displacements at the attachment points, which determine the strength of the equivalent forces. Through dynamical balance at such points, these displacements satisfy a system of linear equations whose coefficients involve the shell displacements generated by on‐surface forces of unit strength, a Green’s‐function problem with both source and observer located on the shell surface. It is thus evident that flexural waves, though subsonic, must be accounted for in the ray acoustic solution to the latter problem. Numerical examples show that they produce high Q intense resonances because of their extremely small radiation damping, which would be dominated by structural damping for dissipative shell material, imprinting their signature in the far field through radiation of the induced forces and carrying much of the information on the internal load. By including the flexural as well as membrane waves, the ray model accurately predicts the induced forces, the shell displacements, and the surface and far‐zone pressures in the frequency range of interest; 1≤ka≤25 (where k is the fluid acoustic wave number and α is the shell mean radius). [Work supported by ONR.]

This paper applies the spectral theory to the formulation of both the pressure field and the displacements of a source‐excited cylindrical shell with the internal attachment of a mass‐spring substructure at two arbitrary locations. Respective alternative representations in the series and integral forms, with a distinct correspondence between each other, may be readily written down. The series form generalizes Guo’s solution which is limited to the diametrical attachment of the spring to the shell [Y. P. Guo, J. Acoust. Soc. Am. 91, 926–938 (1992)], while the integral form is suitable for further ray acoustic reductions which are also affected here. Furthermore, the internal loading is equivalent to the spring‐shell interaction forces acting at the attachment locations. The radiation from the induced forces superimposed with the contribution due to the empty shell then gives rise to the total structural and acoustic responses of the internal‐shell‐fluid system. The equivalent forces, which in general have both normal and tangential components, are functions of the shell displacements at the attachments; the latter may be in turn determined from their continuity conditions and evaluated either by normal‐mode series or the geometrical acoustics fields and shell guided modes. [Work supported by ONR.]

Combining the available ray acoustic algorithms descriptive of submerged thin cylindrical and spherical shells, this paper formulates the pressure and velocity distributions on a hemispherically capped cylindrical shell insonified by an obliquely incident acoustic plane wave. As the first ray acoustic model for a noncanonical shell geometry of considerable current interest, it neglects wave coupling and diffraction due to curvature discontinuities at the junctures as well as contributions from the leaky waves excited through the endcaps. This might be justifiable, because the junctions are not sharp edges (i.e., the normals are continuous) and because the cylinder under consideration is very long compared to the radius. By matching the surface wave vector along the joints, however, due account is taken of leaky wave propagation on, and radiation from, the hemispheres. The total pressure or velocity—their ray constituents are related to each other by appropriate impedances—on the cylinder is then synthesiz...

The ray‐acoustic formulation developed previously for a thin elastic cylindrical shell [Felsen et al., J. Acoust. Soc. Am. 87, 554–569 (1990)] is subject to extensive numerical tests for both on‐ and off‐surface sources, i.e., plane waves, which incidence may be normal or oblique to the axis of cylinder, and phased line sources located on or near the shell surface. The Fresnel transition function is employed to account for the saddle point‐near‐pole effect which arises when the incidence angle is close to the mode angle. As functions of frequency, the amplitude and phase of the pressure field are computed in the range of κa=2 to 50, where κ is the transverse component of the acoustic wavenumber and a is the shell radius, at particular observation angles; whereas the field pattern, parametrized by κa, is established along the azimuthal direction. The ray field agrees well with the reference solution (normal modes) in both cases. Furthermore, the constituent ray‐acoustic components, especially shell‐guided ...