On Peculiarities of Propagation of a Plane Elastic Wave through a Gradient Anisotropic Layer

The problem of diffraction of a plane elastic wave by an anisotropic layer is studied. The diffraction problem is reduced to a boundary value problem for the layer. The grid method is used for solving the resulting boundary value problem. The diffraction of a plane longitudinal wave by the layer is considered. Some peculiarities of the gain-frequency and the gain-angle characteristics of a normal component of an energy flow of a passed longitudinal wave are numerically studied.

Elastodynamic Response of a Chain of Particles

The reflection of an axially incident plane longitudinal wave from a linear chain of identical spherical inclusions embedded in a viscoelastic matrix is measured. The reflection spectrum is characterized by a sequence of resonances corresponding to the Floquet condition, where an integral number of half-wavelengths in the matrix spans the interparticle distance.

Nonaxisymmetric Dynamic Response of Imperfectly Bonded Buried Fluid-Filled Orthotropic Cylindrical Shells

This paper is concerned with the nonaxisymmetric dynamic response of an imperfectly bonded fluid-filled buried orthotropic cylindrical shell excited by a plane longitudinal wave. A thick shell model, including the effect of shear deformation and rotary inertia, has been taken. For the wave propagation in the fluid inside the pipe, linear acoustic equation has been used. The effects of fluid presence on the shell displacements have been studied for different soil conditions and at various angles of incidence of the longitudinal wave. The effects of bond imperfection on the shell response have been compared with the effects realized due to the presence of fluid inside the pipeline. Effects of changes in the fluid density are also discussed. It is found that magnitude of the response of fluid-filled pipeline can become even more than that of an empty pipeline (without fluid), and, hence, it cannot be assumed that a fluid-filled pipeline will always furnish safe and conservative response.

Axisymmetric Scattering of a Plane Longitudinal Wave by a Circular Crack in a Transversely Isotropic Solid

The scattering of elastic waves by a circular crack situated in a transversely isotropic solid is studied here. The axis of material symmetry and the axis of the crack coincides. The incident wave is taken as a plane longitudinal wave propagating perpendicular to the crack surface. A Hankel transform representation of the scattered field is used, and after some manipulations using the boundary conditions this leads to an integral equation over the crack for the displacement jump across the crack. This jump is expanded in a series of Legendre polynomials which fulfill the correct edge condition and the integral equation is projected on the same set of Legendre polynomials. The far field is computed by the stationary phase method. A few numerical computations are carried out for both isotropic and anisotropic solids. Results for the isotropic solid compare favorably with those available in the literature.