Vijay K. Varadan

Frequency dependence of elastic (SH-) wave velocity and attenuation in anisotropic two phase media

Abstract The propagation and attenuation of elastic waves in a random anisotropic two-phase medium is studied using statistical averaging procedures and a self-consistent multiple scattering theory. The specific geometry and orientation of the inhomogeneities (second phase) are incorporated into the formulation via the scattering matrix of each inhomogeneity. The anisotropy of the composite medium is due to the specific orientation of the non-symmetric inclusions. At low frequencies, analytical expressions are derived for the effective wave number in the average medium as a function of the geometry and the material properties and the angle of orientation of the inclusions. The results for the special cases of oriented cracks may find applications in geophysics and material science. The formulation is ideally suited for numerical computation at higher frequencies as evidenced by the results presented for composites reinforced by fibers of elliptical cross section.

Frequency dependent dielectric constants of discrete random media

Numerical computations of the effective dielectric constant of discrete random media are presented as a function of frequency. Such media have a complex dielectric constant giving rise to absorption of a propagating wave both due to geometric dispersion or multiple scattering as well as absorption, if any, due to the viscosity of the particles and the matrix medium. We are concerned with the absorption due to multiple scattering. The scattering characteristics of the individual particles are described by a transition or T-matrix. The effects of two models of the pair correlation function which arises in the multiple scattering analysis are considered. Pie conclude that the well stirred approximation (WSA) is good for sparse concentrations and/or high frequencies whereas the Percus-Yevick approximation (P-YA) is preferred for higher concentrations.

Scattering of acoustic waves by elastic and viscoelastic obstacles immersed in a fluid

Abstract A scattering or T -matrix approach is presented for studying the scattering of acoustic waves by elastic and viscoelastic obstacles immersed in a fluid. A Kelvin-Voigt model is used to obtain the complex elastic moduli of the viscoelastic solid. The T -matris formulation is somewhat complicated because the wave equations and fields are quite different in the solid and fluid regions and are coupled by continuity conditions at the interface. We have obtained fairly extensive numerical results for prolate and oblate spheroids for a variety of scattering geometries. The backscattering, bistatic, absorption and extinction cross-section are presented as a function of the frequency of the incident wave.

Dynamic stress concentrations of cylindrical cavities with sharp and smooth boundaries: I. SH waves

Abstract This paper demonstrates a method for the calculation of the dynamic stress concentration factor when a time-harmonic elastic wave is incident upon a cylindrical cavity of arbitrary cross-section. We discuss in particular a procedure which enables cross-sectional shapes with corners to be examined, although we also consider how shapes with smooth surfaces may be handled. Our method is a computational one, and is based upon Watermans T-matrix formulation. It is shown that for scatterers with corners a piecewise basis must be chosen to represent the surface displacement. The algebraic system of equations obtained from the integral equations and appropriate constraints on the basis representation are then sufficient to determine the stress concentration uniquely. Results are given for cylindrical cavities with square, elliptic and intersecting circular cross sections for SH wave incidence.

Scattering of acoustic waves by elastic and viscoelastic obstacle of arbitary shaped immersed in water

Abstract : A scattering or T-matrix approach is presented for studying the scattering of acoustic waves by elastic and viscoelastic obstacles immersed in a fluid. A Kelvin-Voigt model is used to obtain the complex elastic moduli of the viscoelastic solid. The T-matrix formulation is somewhat complicated because the wave equations and fields are quite different in the solid and fluid regions and are coupled by continuity conditions at the interface. We have obtained fairly extensive numerical results for prolate and oblate spheroids for a variety of scattering geometries. The backscattering, bistatic, absorption and extinction cross-section are presented as a function of the frequency of the incident wave. (Author)

On the application of wave scattering theory for the diagnosis of muscle diseases

Abstract This investigation is concerned with a scattering matrix approach which is proposed for the non-destructive, differential diagnosis of muscle diseases. A number of muscle diseases are classified according to their various pathological indications and appropriate material parameters are derived for utilization as input data for a theoretical model. In the mathematical analysis phase of the model, Watermans T-matrix approach in conjunction with statistical averaging for both position and orientation of muscle fibers are employed to obtain the attenuation due to geometric dispersion for a wide range of frequencies. The numerical results not only exhibit qualitative agreement with existing experimental data for normal muscle but also display differentiable patterns for the various muscle disease cases. The formulation is an improvement over the previously applied scattering theory in that it obtains the attenuation over a continuous frequency spectrum.