H. Überall

Theory of elastic resonance excitation by sound scattering

The resonance formalism of nuclear‐reaction theory is applied to the problem of sound scattering from submerged elastic bodies (illustrated here by circular cylinders and spheres). It is demonstrated that the strongly fluctuating behavior of, e.g., the backscattering cross section is caused by a superposition of generally narrow resonances in the individual normal modes (partial waves), which move up in frequency from one partial wave to the next, corresponding to a series of creeping waves (’’Regge poles’’), and which are superimposed on a background of rigid‐body (potential) scattering. This fact, together with a resonance representation of the elastic field in the interior, indicates that the elastic body is relatively impenetrable to the incident wave except in the vicinity of the resonances, which occur at the eigenfrequencies of the elastic vibrations of the body. Various types of interference between resonance and background are analyzed, and the phase of the partial wave is shown to undergo a jump...

Resonance theory of acoustic waves interacting with an elastic plate

Sound transmission and reflection properties of an elastic layer immersed in a fluid are analyzed by extending the resonance formalism, previously developed by us for the case of a fluid layer [J. Acoust. Soc. Am. 65, 9–14 (1979)]. Resonance expressions for the transmission and reflection coefficients have been obtained both in terms of the frequency‐thickness variable and of the angle‐of‐incidence variable. The resonance positions and widths are explicitly obtained from real equations in terms of given material quantities. Comparison of the resonance theory and exact calculations are given for a steel plate immersed in water. The resonance formalism results show excellent agreement with exact theory in all cases. Interferences between overlapping resonances are clearly identified and analyzed. An examination of the limiting form of the y resonances confirms previous empirical findings of other researchers concerning the frequency‐thickness behavior of the poles and zeroes of the Rayleigh and Lamb resonan...

Surface Waves in Acoustics

Abstract : The article surveys the essential results obtained concerning acoustic surface waves on curved surfaces, and establishes their relationships with the corresponding plane surface waves. In view of the limited generality of the existing literature, the excitation mechanisms considered here for the generation of such surface waves have mostly been taken as those provided by a plane incident acoustic wave; more general mechanisms are briefly mentioned. A classification of surface and lateral waves on flat surfaces, and with a description of their properties is given. Surface waves generated by sound scattering on surfaces of simple or arbitrary curvature, both penetrable and impenetrable is discussed. Theoretical results are considered mainly, but selected illustrative examples of the recent experiments are given also. (Author)

Repulsion of phase‐velocity dispersion curves and the nature of plate vibrations

The Lamb waves propagating in an elastic plate in vacuo generate compressional (L) and shear type (T) plate vibrations that are coupled due to the boundary conditions. Without such coupling, their phase‐velocity dispersion curves would form two intersecting families, which at high frequency tend towards the elastic‐wave speeds CL and CT, respectively. It is shown that the coupling causes a repulsion of the dispersion curves, similar to that encountered in atomic physics for the energy levels of atoms combining into molecules, which prevents their intersection and at the same time exchanges the nature (L↔T) of the underlying vibrations. However, in the repulsion regions a succession of dispersion curves combines to asymptotically approach the uncoupled L or T dispersion curves, respectively. For the case of a plate bounded by fluid on one side, and vacuum on the other, the dispersion curves of the fluid‐borne (Stoneley–Scholte type) wave, which is known from the studies of Grabovska and Talmant to be prese...

Lamb waves and fluid‐borne waves on water‐loaded, air‐filled thin spherical shells

The results of a recent study of fluid‐borne waves on plates with one‐sided fluid loading [M. Talmant, Ph.D. thesis, University of Paris VII (1987)] allow the prediction of the corresponding waves and their resonances (as well as of the Lamb‐wave resonances) on thin submerged spherical shells. Similar fluid waves and the ensuing ‘‘bifurcation’’ in the dispersion curves of the first antisymmetric vibration mode on cylindrical shells were previously described [J. V. Subrahmanyam, Ph.D. thesis, Catholic University of America (1983); J. L. Rousselot, Acustica 58, 291 (1985)] and the fluid waves were observed by Talmant et al. [J. Acoust. Soc. Am. 84, 681–688 (1988)]. The resonances predicted by the plate model for spherical shells are confirmed here by comparison with scattering cross‐section calculations using surface integral equation radiation and scattering (SIERRAS) and T‐matrix codes.

Acoustic resonances of thin cylindrical shells and the resonance scattering theory

An experimental and theoretical study is presented of the properties of circumferential waves on thin‐walled elastic, air‐filled cylindrical shells immersed in water, and of their excitation by normally incident acoustic pulses of short duration. A spectral decomposition of the multiple echo pulses using the Numrich–de Billy method, and subsequent analysis by the resonance scattering theory (RST), reveal for an aluminum shell the presence of an l=2 wave that can be identified with the S0 Lamb wave on a plate, and of an l=0 wave that at low frequencies corresponds to a water‐borne circumferential wave, not given by the Lamb theory of free‐plate vibrations but by its extension to a plate with one‐sided fluid loading. Calculations of complex pole resonances on aluminum and steel shells, as well as of the corresponding circumferential wave speeds and attenuations, serve to clarify the physical situation.

Two Scholte–Stoneley waves on doubly fluid-loaded plates and shells

Previous theoretical and experimental studies of sound scattering from plates and from evacuated cylindrical or spherical shells with one-sided water loading have demonstrated the existence of a water-borne Scholte–Stoneley wave, and its acoustic excitation, in addition to that of the Lamb-type plate or shell wave modes. For two-sided water loading two Scholte–Stoneley waves, of symmetric (S) and antisymmetric (A) nature, were predicted on plates, with only the A wave surviving for the case of one-sided loading, while for loading with two different fluids, again two such waves have been demonstrated theoretically. In the present investigation, these two Scholte–Stoneley waves are studied experimentally via short-pulse scattering from water-immersed, thin-walled cylindrical shells filled alternatingly with air, water, and alcohol, and a theoretical analysis of their dispersion curves is presented.

Resonant scattering of elastic waves from spherical solid inclusions

Previous investigation concerning the scattering of elastic waves from solid spherical inclusions have furnished expressions for the scattering cross sections which, upon numerical evaluation, exhibited resonancelike features as a function of frequency. In the present work, we study these resonances in a fashion suggested by the resonance theory of acoustic scattering due to Flax, Dragonette, and Uberall [J. Acoust. Soc. Am. 63, 723 (1978)]. The resonances of the solid inclusions, exemplified by iron or lucite spheres imbedded in an aluminum matrix, are found numerically in the individual normal‐mode scattering amplitudes, and are interpreted in terms of phase‐matched circumferential waves. Dispersion curves for the phase velocities of the latter are obtained, exhibiting two families of waves of different type. Finally, the connection of these waves with the Stonely waves on the boundary between two flat half‐spaces is noted in high‐frequency limit.

A surface wave interpretation for the resonances of a dielectric sphere

The calculated radar and bistatic cross sections of dielectric spheres exhibit numerous resonances when plotted versus frequency. These resonances may be related to the excitation of electromagnetic eigenvibrations of the sphere, with resonance frequencies calculable from a characteristic equation. It is shown that the resonances may be viewed as originating from families of circumferential (surface, or creeping) waves that are generated during the scattering process; at each eigenfrequency of the sphere, one of these surface waves matches phases after its repeated circumnavigations around the sphere, with the ensuing resonant reinforcement leading to the given scattering resonance. This mechanism explains the existence of electromagnetic eigenvibrations of a general smooth dielectric object; for the case of a sphere, it is shown that the surface waves suffer a phase jump of \pi/2 at each of their two convergence points. We calculated numerical values of the eigenfrequencies of dielectric spheres, and obtain dispersion curves for the phase velocities of the surface waves.

A comparison between the boundary element method and the wave superposition approach for the analysis of the scattered fields from rigid bodies and elastic shells

The steady state analysis of the scattering of plane acoustic waves from submerged rigid and elastic bodies using two approaches is presented. The first approach uses a combined finite element/boundary element (FE/BE) methodology. The NASA structural analysis (NASTRAN) program is used to formulate the structural matrices based on the finite element method (FEM). The surface integral equation radiation and scattering (SIERRAS) program creates the fluid matrices based on the boundary element method (BEM) and solves the coupled fluid-structure interaction problem. A superparametric boundary element (BE) with nine nodes is employed. The combined Helmholtz integral equation formulation (CHIEF) is employed to provide a unique solution for all frequencies. In the second approach, the superposition method (SUP) is used for modeling the fluid. The SUP method is an off-boundary approach that employs a number of point sources moved inside the body to represent the fluid response at the surface. This allows the fluid...