A review of wave motion in anisotropic and cracked elastic-media

The differential-integral equation of motion for the mean wave in a solid material containing embedded cavities or inclusions is derived. It consists of a series of terms of ascending powers of the scattering operator, and is here truncated after the third term. This implies the second-order interactions between scatterers are included but those of the third order are not.The formulae are specialized to the case of thin cracks, either aligned in a single direction or randomly oriented. Expressions for the overall elastic constants are derived for the case of long wavelengths. These expressions are accurate to the second order in the number density of scatterers.

Overall properties of a cracked solid

A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.

Recent Advances in Analysis of Laminated Beams and Plates, Part II: Vibrations and Wave Propagation

Inversion of seismic velocities for the pore aspect ratio spectrum of a rock

Effects of multiple parallel fractures on apparent attenuation of stress waves in rock masses

Self-consistent results on the properties of inhomogeneous materials are compared with results based on multiple scattering calculations for a medium containing either spherical inclusions or cylindrical inclusions. Inconsistencies are found in terms of order c2, where c is the concentration of inclusions. Thus the claims of O'Connell and Budiansky and others regarding the validity of self-consistent calculations for properties of inhomogeneous materials at nondilute concentrations are not supported.

Elastic moduli of two-component systems

The problem of the determination of the overall dynamic elastic moduli of an elastic solid permeated by uniformly distributed penny-shaped cracks is considered. The cracks are assumed to be filled with a viscoelastic material. The orientations of the cracks may be either parallel or perfectly random. The overall velocities as well as the specific attenuation coefficients of plane harmonic compressional and shear waves are calculated for low frequencies and dilute concentration of the cracks.

A. K. Chatterjee

Papers

Elastic moduli of two-component systems

Attenuation of elastic waves in a cracked, fluid-saturated solid

The Elastic Moduli of a Fiber-Reinforced Composite

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