Lawrence Flax

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...

Scattering of an obliquely incident acoustic wave by an infinite cylinder

Expressions are derived for the scattered farfield pressure which results from the illumination of an infinite aluminum cylinder by a plane acoustic wave, whose propagation direction makes an arbitrary angle, α, with the normal to the cylinder axis. Computations are made at angles between α=0 ° and the Rayleigh critical angle, α=31.3 °. Changes in the scattered field are related to shifts in the paths of geometric and elastic surface waves from circumferential at α=0 °, to helical, to axial Rayleigh surface waves generated at the Rayleigh critical angle.

Acoustic reflection from layered elastic absorptive cylinders

The reflection of plane waves by a layered cylindrical shell in water is investigated theoretically. Either or both of the two layers of elastic material may be absorptive. The solution as a function of frequency is examined for several combinations of inner and outer layers.

Acoustic reflection from elastic spheres and rigid spheres and spheroids. II. Transient analysis

Curves relating the reflected acoustic pressures to frequency for a rigid sphere and spheroid and for elastic spheres of aluminum, brass, and tungsten carbide in water are obtained. Experimental measurements using single short acoustic pulseforms are compared with theory. Excellent agreement is obtained for the limited ranges of ka over which the experiments were done. Only the case of monostatic reflection is considered.

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.

Acoustic wave scattering by a finite elastic cylinder in water

Numerical results are obtained for a finite circular elastic cylinder with spherical end caps using Waterman’s T‐matrix method. In addition to the important practical applications that this geometry has in underwater acoustics, for the first time this method is applied to elastic scatterers that have a discontinuity in the first derivative of the normal to the surface. This makes the problem numerically difficult and is a good test of the effectiveness of the T‐matrix method. The frequency dependence of the backscattering cross section is presented for a cylinder whose overall length is twice its diameter. Our results are compared with experiments showing excellent agreement.

Monostatic reflection of a plane wave from an absorbing sphere

The monostatic reflection from a lucite sphere in water is measured and compared with the exact classical scattering theory. Experimental results do not agree with theory which neglects absorption, in direct contrast to the excellent agreement found when metal spheres are used as targets. The theory is modified to include the effects of absorption of shear and compressional waves in lucite, and agreement between experiment and the modified theory is demonstrated.Subject Classification: 20.30, 20.15.

Reflection of elastic waves by a cylindrical cavity in an absorptive medium

The analytical formulation for the total scattering cross section of a cylindrical cavity in an elastic medium is given for the case of inclusion of compressional and shear wave attenuations. Examples are computed of relatively small attenuations exemplified by the material polymethacrylate and relatively large attenuations exemplified by polyethylene. The inclusion of wave attenuations known to exist in these materials cause the scattering cross section to diminish significantly for wave‐number cylindrical‐cavity‐radius product up to 10.

Analysis and computation of the acoustic scattering by an elastic prolate spheroid obtained from the T‐matrix formulation

The T‐matrix formulation is used to compute the form function of an elastic prolate spheroid. The method allows acoustic scattering computations to be made for finite bodies at frequencies into the resonance region, and the lowest order resonance observed is, as expected, due to the excitation of a Rayleigh surface wave.

High ka scattering of elastic cylinders and spheres

Reflection characteristics of elastic cylinders and spheres for large values of ka are determined by explicit evaluation of the wave harmonic series for a nonabsorptive medium.