Mieczysław Cieszko

Acoustic wave propagation in equivalent fluid macroscopically inhomogeneous materials

A one-dimensional problem of propagation of plane harmonic wave in macroscopically inhomogeneous materials is analyzed. A general description is proposed for the material of the equivalent fluid type characterized locally by two acoustical parameters: the wavenumber and the acoustical impedance. The coupled system of ordinary differential equations for amplitudes of forward and backward waves is derived. As an example the problem of wave interaction with a layer of inhomogeneous material placed between two homogeneous halfspaces is considered. The analytical solution and explicit expressions for reflection and transmission coefficients are obtained. It is shown that the presence of the inhomogeneous transition layer causes strong frequency dependence on both coefficients.

Wave dispersion in randomly layered materials

Wave scattering in materials composed of two kinds of alternating layers with different elastic properties and randomly distributed thicknesses has been modeled. The general form of the dispersion equation is derived for the unbounded layered medium. It defines two basic macroscopic characteristics of the scattered wave: phase velocity and attenuation, which are explicit functions of wave frequency and microscopic parameters of the system: acoustic properties of the layers and stochastic characteristics of their thickness distributions. The analytical expressions are derived for three special cases: for long waves; for a periodic medium composed of layers with constant thicknesses and for random medium with uniform distribution of layer thicknesses. Special attention is paid to the analysis of the frequency dependence of the wave parameters. It was shown that the predictions of the model for long waves and for periodic medium are compatible with the results obtained in the literature. Moreover, comparison...

The fundamentals of low-frequency ultrasound for diagnosis of bone tissue

The subject of the paper is presentation of theoretical and methodological fundamentals for a novel low-frequency ultrasonic method of identification of macroscopic mechanical properties and parameters of macroscopic inhomogeneity of bone tissue. The issue is directly associated with non-invasive assessment of bone fracture risk, being result of the diseases such as osteoporosis, osteomalacia, osteopenia etc. In the present paper the heel bone is modeled as a set of three-layers characterized by continuously inhomogeneous distribution of acoustical properties. The border between the cortical and cancellous bone in calcaneus is not sharp, thus at the distance about 1 cm there is observed the transition region with gradual changes of the properties from the low porosity cortical bones to the high porosity cancellous bone. As the length of transition region is on the order of a few centimeters the low frequency ultrasound (50-200 kHz) is required to be sensitive to this size of inhomogeneity. Identification of the lamination parameters of calcaneal bone (e.g. length of transition regions) and the mechanical (acoustical) properties of each inhomogeneous layer is the crucial element of the proposed novel diagnostic method.

To what extent randomly layered material can be used for modelling ultrasonic wave propagation in cancellous bone

It has been suggested that a periodical two-layered medium might by considered as the simplified model of wave propagation in cancellous bone. In the present paper an approach is proposed to describe a one-dimensional problem of wave propagation in the cancellous bone modeled as a randomly layered material composed of two kinds of alternating elastic layers having randomly distributed thicknesses and different acoustic properties. A compact form of the dispersion equation and the relationships for reflection coefficients and acoustic impedance of the randomly layered medium is obtained. The wave parameters are functions of acoustical properties of the layers and the distributions of their thicknesses. The obtained equations are used to derive the analytical expressions for three special cases: for long waves; for a periodic medium composed of layers of constant thicknesses; and for random medium characterized by uniform distribution of layer thicknesses. Special attention is paid to the frequency analysis of the wave parameters characterized by strong and weak acoustic inhomogeneity. It is shown that although the developed model is a rough simplification of the cancellous bone architecture, it has potential for future research, particularly for higher frequency range, when the scattering effects play the predominant role in wave attenuation.

Scattering of ultrasonic waves in randomly layered materials

The goal of the paper is the proposal of a new macroscopic description of scattering of elastic waves at internal inhomogeneities of the material. Within the studies the microscopic inhomogeneity of the medium is modeled as the alternately arranged two kinds of elastic layers of random thicknesses and different mechanical properties. Calculations of the acoustical characteristics of such medium (reflection and transmission coefficients) are performed in two stages: (i) first the problem of interaction of plane harmonic wave with the half space of the randomly layered medium for the case of normal wave incidence is analyzed; (ii) then the interaction of the harmonic wave with the slice composed of randomly layered structure is considered. Such approach allowed to derive analytical relations for the phase velocity of wave propagation and attenuation as the explicit functions of frequency, stochastic structural parameters of the medium and material properties of layers. The obtained formulas are helpful for ...