Transient dynamic analysis of a fluid-saturated porous gradient elastic column

The dynamic response of a fluid-saturated porous gradient elastic column to a transient disturbance is determined analytically and numerically. The basic dynamic theory of a fluid-saturated poroelastic medium due to Biot is modified by replacing the classical linear elastic model of the solid skeleton by the simple gradient elastic model of Mindlin with just one elastic constant (internal length scale) in addition to the classical ones. Thus, the new theory, which is presently restricted to the one-dimensional case, can take into account the microstructural effects of the solid skeleton. After the establishment of appropriate boundary and initial conditions, the one-dimensional dynamic column problem is solved analytically with the aid of the Laplace transform with respect to time. The time domain response is finally obtained by a numerical inversion of the transformed solution. The effect of the solid microstructure on the response is assessed and discussed.     

The propagation of Love waves in a fluid-saturated porous anisotropic layer

Summary The paper concerns the propagation of Love waves in a transverse-isotropic fluid-saturated porous layer overlaying an elastic nonhomogeneous half-space. Using the Biot's theory for the porous layer and the theory of elasticity for the lower medium, the dispersion equation has been derived. This complex transcendental equation that relates frequency, phase velocity, anisotropy factor of the layer and the inhomogeneity character of the half-space has been solved with the aid of successive approximation method. The effect of anisotropy and heterogeneity has been shown graphically.With 2 Figures     

Propagation of elastic waves in a micropolar sphere

The problem of harmonic wave propagation in a solid micropolar sphere is solved by considering the two scalar and two vector equations governing the motion. Stress free boundary conditions are applied and a characteristic equation is obtained. The characteristic determinant can be resolved into the product of two independent determinants. Two classes of motion are observed which have been analysed in detail.     

On propagation of shear waves in a multilayer medium including a fluid-saturated porous stratum

Summary The propagation of SH-type waves in a double surface layered medium with an intermediate transverse-isotropic fluid-saturated porous stratum has been examined. The top-most layer is assumed to be impermeable, elastic, homogeneous and isotropic, whereas the lower half-space is a nonhomogeneous one. The dispersion equation has been derived using the Biot's theory for the porous layer and the theory of elasticity for both the upper and the subjacent half-space.The corresponding dispersion equation for the simplified case where the dissipation caused by the relative fluid flow has been omitted has also been obtained. The numerical results obtained for this simplified case have been shown graphically.With 5 Figures     

On internal coupling in dynamic equations of fluid-saturated porous solid

Dynamic equations of a porous solid-fluid mixture have been studied accounting for the influence of the pore structure. It is shown that when a skeleton pore structure is characterized by two parameters volume porosity and the structural permeability tensor, the mixture can be considered as composed either of two physical components—the porous solid and the fluid, or two kinematic components—the first being the skeleton and the fluid trapped within, the second being the unimpeded fluid. During a deformation process, mass exchange between the kinematic components may appear, thus provoking the inertial coupling between them. The kinematic division of the solid-fluid mixture, contrary to the physical division, enables one to formulate the appropriate motion equations which include this inertial coupling.     

Propagation of elastic waves through a discontinuity in a medium

The work was supported by the Russian Fund of Fundamental Investigations (project code 93-05-9577).     

Influence of the squirt flow on reflection and refraction of elastic waves at a fluid/fluid-saturated poroelastic solid interface

In this paper, the reflection and refraction problem of a plane wave moving in perfect fluid incident on a viscous fluid-saturated poroelastic solid is investigated. Attention is focus on the effect of squirt flow on the reflection and refraction coefficients predicted by BISQ model. The variations of these coefficients with the characteristic squirt flow length have been shown graphically. The results are also compared with those based on Biot theory without considering the squirt flow effects. The results indicate that the effect of the squirt flow is noticeable in the reflection and refraction phenomenon.     

DQEM for analyzing dynamic characteristics of layered fluid-saturated porous elastic media

Based on the Porous Media Theory presented by de Boer, the governing differential equations for a layered space-axisymmetrical fluid-saturated porous elastic body are firstly established, in which the suitable interface conditions between layers are presented. Then, a differential quadrature element method (DQEM) is developed, and the DQEM and the second-order backward difference scheme are applied to discretize the governing differential equations of the problem in the spatial and temporal domain, respectively. In order to show the validity of the present analysis, the dynamic response of a fluid-saturated porous medium is analyzed, and the obtained numerical results are directly compared with the existing analytical results. The effects of the numbers of the elements and grid points on the convergence of the numerical results are considered. Finally, the dynamic characteristics of a layered fluid-saturated elastic soil cylinder subjected to a water pressure or a dynamic loading are studied, and the effects of material parameters are considered in detail. From the above numerical results, it can be found that the DQEM has advantages, such as little amount in computation, good stability and convergence as well as high accuracy, so it is a very efficient method for solving the problems in soil mechanics, especially such problems with discontinuities.     

Plane waves in a rotating elastic solid with voids

Plane waves in a linear, homogeneous and isotropic unbounded clastic solid containing a distribution of vacuous pores (voids) and rotating with a uniform angular velocity are studied. The effects of rotation of the body on the phase speed, energy loss and decay coefficient are analysed in some detail for small and large frequency dilatational waves influenced by the presence of voids. Results obtained earlier are recovered as particular cases of the more general results obtained here.     

Propagation of acceleration waves in micropolar elastic solids

The propagation and growth of acceleration waves of arbitrary form propagating into a deformed micropolar elastic solid are investigated. The speeds of propagation are obtained for isotropic micropolar elastic materials and the growth equation is established. The growth equation of acceleration wave is integrated in the case of principle waves for isotropic materials and the decay conditions are examined for both macro- and micro-amplitudes.     

Propagation of acoustic waves in unsaturated porous media

A mathematical model of propagation of acoustic waves in a proous medium saturated with a two-phase mixture is proposed. The mechanism of initiation of slow motion as a result of prolonged nondestructive acoustic action is analyzed. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 3, pp. 433–440, May–June, 1998.     

Nonlinear surface waves on an elastic solid

The effect of quadratic elastic nonlinearity on the propagation of surface Rayleigh waves on an isotropic elastic solid is examined. Using the method of multiple scales an approximate solution is obtained which is uniformly valid in both spatial directions as well as in time. An arbitrary wave profile is considered and an integro-differential equation is derived for the Fourier transform of the displacement on the boundary. In the case of a quasi-monochromatic wave explicit expressions are derived for the variations of the amplitudes of the fundamental and second and third harmonics along the boundary.     

Surface wave propagation in a fluid-saturated incompressible porous medium

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.     

Radial propagation of rotary shear waves in a finitely deformed elastic solid

A study is made of the radial propagation of rotary shear waves in an incompressible elastic solid under finite radial deformations. Basic equations are derived on the basis of Biot's mechanics of incremental deformations, and analysis is made by specializing the initial deformations to two cases: (a) an infinite solid with a cylindrical bore is inflated by all-around tension, and (b) a cuboid is rounded into a ring and its ends are bonded to each other. The influence of the inhomogeneities of such deformations upon the laws of shear wave propagation is presented in the form of curves.     

A note on infinitesimal shear waves in a finitely deformed elastic solid

In the present note we discuss a class of small dynamic deformations imposed on a large static deformation. A semi-inverse method is used to obtain the equations of motion for the small deformations in a simple manner. The results are used to extend known results for a tube of hyperelastic material subject to inflation and extension, when additional telescopic and rotational shears are applied.     

Propagation of axisymmetric waves on the surface of a cylindrical cavity in elastic medium

A nondamped axisymmetric mode that propagates in an elastic cylindrical waveguide representing an extended cavity with a circular cross section in an infinite homogeneous medium is described. The wave dispersion in this system is analyzed and the similarity with and differences from other elastic media with one boundary are considered, including an infinite round rod and the surface of a half-space (Rayleigh wave). It is shown that, for axisymmetric waves in the cavity, a boundary frequency dependent on the curvature radius always exists, below which the waves are evanescent. A physical interpretation of results is given.     

Propagation of waves of metal-hydride thermal conversion in blown-through porous media

A method of metal-hydride thermal conversion that is an alternative to the traditional method is proposed and investigated. The unlike poles of metal-hydride thermal converters are distributed in pairs inside parallel channels. The channels are blown through with a heat-transfer agent. Thermal conversion develops as a set of successive heat waves. By a numerical-modeling method it is shown that the maximum thermal effect is attained in synchronous motion of the heat wave and the heat source (or sink) that accompanies the phase transition in the succession of metal-hydride poles. The results are presented in a form convenient for prediction of the thermal and energy efficiency of the proposed thermal-conversion method in real devices. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 1, pp. 51–61, January–February, 1998.     

Propagation of Love waves in an elastic layer with void pores

The paper presents a study of propagation of Love waves in a poroelastic layer resting over a poro-elastic half-space. Pores contain nothing of mechanical or energetic significance. The study reveals that such a medium transmits two types of love waves. The first front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the love wave in an elastic layer over an elastic half-space. The second front depends upon the change in volume fraction of the pores. As the first front is well-known, the second front has been investigated numerically for different values of void parameters. It is observed that the second front is many times faster than the shear wave in the void medium due to change in volume fraction of the pores and is significant