Reflection and transmission of seismic waves at the boundaries of porous media

The mode conversions which occur during the reflection and transmission of seismic waves at the boundaries of porous media are analysed. It is shown how the energy partitioned to the various modes depends on the incident angle and on the physical properties of the fluid and solid components on each side of the boundary. The boundary conditions used here predict the occurrence of bright and dark spots as are currently observed in seismic studies of heavy oil reservoirs. They also give rise to a class of pseudo interface waves which propagate in a direction almost parallel to the surface and which become true interface waves in the limiting case where the porous media degenerate to elastic solids. When thermomechanical coupling is an important attenaution mechanism in one of the media it is also observed to have a substantial effect on the mode conversions which occur at the boundary.     

Modelling of fibre pull-out in cracked fibre reinforced composites with linear elastic fracture mechanics

A method of finite element modelling the fracture mechanics of a fibre reinforced cement composite is presented. It embodies the use of beam elements with negative extensional stiffness. The method compares favourably with experimental work. Whilst fibre reinforced cement composites are used in this work, the techniques used are applicable to any type of fibre composite material.     

Spherical blast waves in multicomponent media

The solution of the problem of propagation of a wave in soils is presented for the case when the wave is produced by the detonation of a spherical charge of some explosive material (EM). The solution is obtained on a computer by the method of characteristics. The soils are regarded as multicomponent media consisting of solid particles, water, and air in conformity with the model proposed in [1, 2]. The dependence of the pressure, velocity of the particles, and the density in the wave front on the distance is determined; the variation of these parameters with time at fixed points of the medium is also determined. The results are compared with the results of tests [1, 2]. Their close agreement for different contents of the components indicates the applicability of the multicomponent model to soils. The limits of applicability of the model are determined. The propagation of a plane wave under the same conditions was investigated in [3].     

Linear waves in saturated porous media

The peculiarity of linear and nonlinear wave propagation in porous media saturated with liquid or gas has been investigated by the methods of multiphase media mechanics. It has been shown that for the analysis and interpretation of experimental data, it is expedient to build models taking into account the nonstationary powers of interaction between the solid and liquid phases and the viscouselastic behaviour of the porous media skeleton. Inertia and inertia-viscous powers principally influence wave attentuation in porous media. Two interphase mechanisms of momentum transfer (two stress tensors — in the solid phase and liquid) lead to two types of waves. Attenuation is determined not only by interphase friction, but also by dissipation resulting from intergrain friction in the solid phase, the influence of which multiplexly exceeds the liquid viscosity influence. The real decrement of attenuation may exceed the sphere restricted by the limiting curves corresponding to the frozen and equilibrium schemes of intergrain deformation. The attenuation of momentum perturbation has been studied. The method of discrete Fourier transform has been used. The analysis of experimental data contained in the literature and their comparison with the results of calculations has been carried out.     

Precursors for waves in random media

We consider scattering of a pulse propagating through a three-dimensional random media and study the shape of the pulse in the parabolic approximation. We show that, similarly to the one-dimensional O’Doherty–Anstey theory, the pulse undergoes a deterministic broadening. Its amplitude decays only algebraically and not exponentially in time, due to the signal low/midrange frequency component. We also argue that the parabolic approximation captures the front evolution (but not the signal away from the front) correctly even in the fully three-dimensional situation.     

Decaying surface waves in inhomogeneous media

Two problems on plane decaying surface waves in an inhomogeneous medium are under consideration: the problem where the waves similar to Rayleigh waves propagate in an isotropic elastic half-space that borders with a layer of an ideal incompressible fluid and the problem where the waves similar to Love waves propagate in a semi-infinite saturated porous medium that borders with a layer of an isotropic elastic medium.     

Guided electromagnetic waves in anisotropic media

Summary The propagation of guided waves in anisotropic media has recently become of interest in two fields, viz. in the interpretation of ferromagnetic resonance experiments and in the construction of microwave fourpoles which violate the reciprocity relation. In both cases we are faced with the solution of Maxwell's equations in a volume which is enclosed by perfectly conducting walls and which is completely or partially filled with a medium whose magnetic permeability is described by a second order tensor. An account is given here of some work, both theoretical and experimental, on this subject. Chapter I is an introduction, containing a short survey of the theory of guided waves in isotropic media and of the problems arising in anisotropic media, together with a historical synopsis. Chapter II gives a general formulation of the theory of guided waves in anisotropic media, comprising the existing theories, and also deals with some new applications. In Chapter III a cavity technique for measuring Faraday rotations is described which has several advantages over older techniques. In Chapter IV experimental results obtained for the series of Ferroxcubes IVA, B, C, D, E are collected. Chapter V finally deals with the physical interpretation of these results. In particular the experimental data are compared with Rado's theory of the permeability tensor in non-saturated ferromagnetics.     

Structure of permanent waves in density-stratified media

Non-linear steady waves in density-stratified channels are discussed. Under the assumption of non-diffusive incompressible flow, a method to classify all waveforms is given for moderate wave amplitudes, when the densityq at infinity decreases with altitude (q<0). The classification is worked out explicitly for the two highest critical Froude numbers. Furthermore, special density distributions are constructed with the purpose of showing that, for example, solitary waves exist even ifq>0.Dedicated to Professor Gaetano Fichera on the occasion of his 70th birthday. General lecture delivered at the 11th Italian National Congress of Theoretical and Applied Mechanics (AIMETA), Trento, September 1992.     

Propagation of combustion waves in bubbly media

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 165–166, March–April, 1992.     

Coupled elastic waves in uniform isotropic media

This article deals with a certain type of wave in an infinite elastic medium. In contrast to ordinary longitudinal and transverse waves, the amplitude of the type of wave in question depends sinusoidally on the coordinates of a plane which is transverse to the direction of propagation of the wave, i.e., the wave is actually a packet of travelling and stationary waves. Longitudinal waves of this type are always coupled with transverse waves, while transverse waves of the given type may be coupled with longitudinal waves or another transverse wave or may exist as a single wave in the form of a packet containing a travelling wave and a stationary wave. The coupled waves have two phase velocities, which depend on the mechanical properties of the medium, the frequency of vibration, and the wave numbers of the stationary waves. Coupled surface waves in an elastic medium are more general in character than Rayleigh waves; they exhibit dispersion, and they can be used to explain certain seismological observations made during earthquakes—the complete absence of vertical displacements in some cases and the frequent occurrence of horizontal displacements parallel to the wave front. Allowing for the coupling of elastic waves in a layer leads to a more general characteristic equation than the equation obtained in the Rayleigh-Lamb problem. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 19–28, September, 1999.