A theory is presented for the calculation of the acoustic material signature of a multilayered elastic half-space overlain by a fluid. The solid layers are composed of homogeneous isotropic linearly elastic materials and are firmly bonded at the interfaces. The calculation procedure is valid at an arbitrarily high frequency of excitation. Results are presented for a uniform, a single layered and a four layered model of the half-space at two frequencies of excitation; one moderate (35 MHz) and the other relatively high (370 MHz). Several new features of the material signatures and their possible use in the material characterization of layered specimen are indicated.

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In this paper, a mathematical formulation is presented to compute the V(z) of a tapering layered solid and applying this formulation to the determination of acoustic properties of biological cells and tissues. The formulation is adopted in the simplex inversion algorithm to obtain the acoustic properties of a tapering cell from its V(z) values. The influence of two parameters had been considered: The tapering angle and the presence of a thin liquid layer present between cells and the substratum to which they adhere. Up to a tapering angle less than 10 degrees, it can be safely neglected. However, if a larger angle is neglected, then the acoustic wave velocity in the cell is overestimated. Cell thickness estimation is not affected significantly when the tapering angle is ignored. The calculations of acoustic properties of cells are considerably influenced by the introduction of a thin fluid layer between the solid substratum and the overlying cell, neglecting the presence of at least a very thin layer (20-30 nm), in general, results in a considerable overestimation of sound velocity. The reliability of the data calculated from V(z) values was ascertained using an independent method to determine cell thickness by calculating it from the interference fringe pattern obtained with the reflection-interference light microscope. The shape of the glutaraldehyde-fixed cells was similar to fried eggs. The highest sound velocities were found close to the periphery of the dome-shaped cell center. In the very center and over most of the area of the thin periphery, sound velocity was close to that in saline.

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A simpli"ed model is presented to predict the strength variations of brittle matrix composites, reinforced by steel "bres, with the variations of "bre parameters*length, diameter and volume fraction. This model predicts that its tensile and #exural strength increase non-linearly with the "bre volume fraction. It also predicts that similar non-linear behaviour should be observed with the reduction of the "bre diameter when other parameters are kept constant. The experimental results support both these theoretical predictions. It is also explained why an increase in the "bre length does not always signi"cantly increase the fracture toughness. The objective of this paper is not to explain and understand in great detail the science of all phenomena responsible for the strength increase of "bre reinforced brittle matrix composites, but to provide a simple engineering explanation as to why its strength increases with the "bre addition, and how this increase can be quantitatively related to the variations in "bre parameters*"bre volume fraction, "bre length and diameter. These simplifying steps are needed to provide a tool that the practicing engineers can use to predict the brittle matrix strength variation with the "bre parameters. In the area of geomechanics, the results presented here can be used to assess and predict the behaviour of "bre-reinforced earth.