No abstract

The scattering of plane compressional waves by a spherical obstacle in an elastic solid, which was investigated by Ying and Truell is examined further. For a rigid inclusion, the boundary conditions are redefined to take into consideration the motion of the inclusion inside the solid. By a proper limiting process, it is shown that the solutions for a rigid insert, a fluid sphere, a cavity, or an obstacle in a fluid are all derivable from the general results of an elastic inclusion. The rates of energy scattering due to a small rigid obstacle (a«λ) are found to be inversely proportional to the fourth power of wavelength.

The problem of dynamic stresses and displacements around a cavity and rigid inclusion of arbitrary density is examined for an elastic medium during the passage of a plane shear wave. In the cavity case, the dynamic stresses and displacements are found to be dependent upon the incident wave number and Poisson’s ratio of the medium. In the rigid-inclusion case it is found that dynamic stresses and the rigid-body rotation and translation are dependent upon the incident wave numbers, the Poisson’s ratio, and the density ratio of the medium and the insert. Close coupling is observed between the stresses and the rigid-body motion of the insert.

The transient response of a rigid spherical inclusion of arbitrary density embedded in an elastic medium owing to an incident pulse is examined in this paper. The Fourier-integral method is used, and an exact solution of the response is obtained. It is found that the acceleration and velocity of the inclusion are substantially different from those of the medium. A slight difference in the time history of the displacement between the inclusion and the medium is also noted.

A theory of the spectral analysis of the scattering of elastic waves is presented and illustrated with numerical results for the scattering by a circular cylindrical fluid inclusion in a solid. When the spectral frequencies are nearly equal to the real parts of the principal frequencies of the fluid inclusion in free vibration, the power spectrum of the scattered pulses undergoes a rapid rise and fall in magnitude because of the selective transmission of an incident wave. The conspicuous peaks and valleys of the backward and forward scattering spectra can be identified with the overtone frequencies of the two lowest normal modes of the cylinder, from which the characteristics of the fluid inclusion, the ratio of the wave speed to radius, can be determined. Subject Classification: [43]20.15, [43]20.30.