Propagation of torsional waves in tubular bones

By considering the material inhomogeneity and anisotropy of osseous tissues, the propagation of torsional waves in tubular bones has been studied in this paper. An exact closed form solution is presented. The electric and magnetic fields induced by the travelling torsional waves in tubular bones are also derived by accounting for the piezoelectricity of osseous material. Making use of the derived analytical solution, and the experimentally determined constants for osseous tissues, numerical values of the phase velocities and attenuation coefficients are calculated for different frequencies in the ultrasonic range. Further, the effects of material damping and inhomogeneity on the attenuation and phase velocities of the waves are examined.     

Guided ultrasonic waves in composite cylinders

The ultrasonic nondestructive evaluation of composite cylinders requires a thorough understanding of the propagation of waves in these materials. In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied. The frequency equations obtained for free cylinders and the effect of increased fiber volume fraction (increased anisotropy) on the dispersion characteristics of the rod are explored. The numerical results reveal a number of previously unnoticed characteristics of dispersion curves for composite cylinders. The mode shapes of longitudinal waves propagating in glass/epoxy cylinders are also plotted. These plots can be used to choose an appropriate strategy for inspecting composite cylinders by ultrasonic nondestructive evaluation techniques. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 411–426, May–June, 2007.     

Use of ultrasonic surface waves for studying the properties of the human tibia

A method of determining the ultrasonic surface-wave velocity by means of exponential concentrators is proposed for determining the properties of human tibia in vitro. The effect of the radiation frequency and the thickness of the surface layer of bone tissue on the surface-wave propagation velocity is studied. For measurement purposes the tibia is divided into 24–28 vertical levels and six to seven horizontal zones. The variation of the surface-wave velocity with the measuring point is investigated. Relations are established between the distribution of surface-wave velocities and the statistical parameters characterizing the dispersion of the results, on the one hand, and biological age and the source of the bone (right or left leg), on the other.     

The propagation of ultrasonic waves in piezoelectric semiconductors

The equations of wave propagation in piezoelectric semiconductors have been derived for a frame of reference in which the principal axes concide with the crystallographic axes. It is shown that generally the dispersion relation is given by a determinant of order six but under condition wherein the plasma modes are not excited, it could be reduced to a determinant of order five, which is equivalent to the one given by Hutson and White. The dispersion relation for hybrid waves which couple acoustic phonons with plasmons has been derived and this is shown to be given by a determinental equation of order four.     

A study of Langmuir waves in plasmas

This paper talks about Langmuir waves in plasmas. The integration of the governing nonlinear Schrödinger’s equation with perturbation terms is carried out. Both Kerr law as well as the power law nonlinearity are considered.     

A numerical study of electromagnetic waves in periodic waveguides

Here are considered time‐harmonic electromagnetic waves in a quadratic waveguide consisting of a periodic dielectric core enclosed by conducting walls. The permittivity function may be smooth or have jumps. The electromagnetic field is given by a magnetic vector potential in Lorenz gauge, and defined on a Floquet cell. The Helmholtz operator is approximated by a Chebyshev collocation, Fourier–Galerkin method. Laurent's rule and the inverse rule are employed for the representation of Fourier coefficients of products of functions. The computations yield, for known wavenumbers, values of the first few eigenfrequencies of the field. In general, the dispersion curves exhibit band gaps. Field patterns are identified as transverse electric, TE, transverse magnetic, TM, or hybrid modes. Maxwell's equations are fulfilled. A few trivial solutions appear when the permittivity varies in the guiding direction and across it. The results of the present method are consistent with exact results and with those obtained by a low‐order finite element software. The present method is more efficient than the low‐order finite element method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 490–513, 2014     

A study of bending waves in infinite and anisotropic plates

In this paper we present a unified approach to obtain integral representation formulas for describing the propagation of bending waves in infinite plates. The general anisotropic case is included and both new and well-known formulas are obtained in special cases (e.g. the classical Boussinesq formula). The formulas we have derived have been compared with experimental data and the coincidence is very good in all cases.