Wave propagation in fractured porous media

A theory of wave propagation in fractured porous media is presented based on the double-porosity concept. The macroscopic constitutive relations and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. In microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law in fractured porous media. The macroscopic constitutive relations of elastic porous media saturated by one or two fluids and saturated fractured porous media can be obtained from the constitutive relations developed in the paper. In the simplest case, the final set of governing equations reduce to Biot's equations containing the same parameters as of Biot and Willis.Now at Izmir Institute of Technology, Anafartalar Cad. 904, Basmane 35230, Izmir, Turkey.     

FFT-based spectral analysis methodology for one-dimensional wave propagation in poroelastic media

The general one-dimensional equilibrium equations describing the dynamic behaviour of a porous medium form a system of coupled hyperbolic partial differential equations. A transition from the time to the frequency domain is made by spectral decomposition of the displacements. The equations simplify to a set of coupled ordinary differential equations. A solution can be obtained by solving a frequency-dependent eigenvalue problem. The characteristic equation clarifies the double wave-pattern and the attenuation of each wave. A spectrally formulated element uses the frequency-dependent eivenvectors as shape functions. The mass distribution is treated exactly without the need of subdividing a member into smaller elements and therefore wave propagation within an element is also treated exactly.     

Wave propagation in anisotropic media with non-local elasticity

In an effort to understand and quantify the effect of non-local elasticity on the wave propagation response of laminated composite layered media, a frequency-wavenumber domain based finite element method is employed. The developed elements are based on the exact solution in the transformed domain and thus exactly represent the dynamics of a layer. This feature enables to model a layer of any thickness by a single element and drastically reduces the cost of computation. The effect of non-locality on the dispersion relation and in turn on the wave response is compared with local (classical) elasticity solutions. A procedure and sample example is outlined to estimate the magnitude of the non-locality parameter by comparing the dispersion relation with lattice dynamics. The effect of non-locality, in terms of the mode-shift and appearance of dispersion on the modes of Lamb waves is further demonstrated.     

Wave propagation and resonance phenomena in inhomogeneous media

The waveguide and resonance properties of inhomogeneous penetrable one–dimensional–periodical structures that consist of two different media are studied within the framework of a one–dimensional approximation. The pass and stop bands are determined. A dispersion relation for all the waveguide modes is obtained. Explicit expressions for low waveguide frequencies and corresponding phase velocities of waveguide modes for mono– and polydisperse media are found. The influence of the polydispersity of the sizes of heterogeneities on the low frequencies of a pass band is considered. A pass band in the range of low frequencies is detected. It is shown that the polydispersity does not affect the waveguide properties of a medium at low frequencies of the first pass band. The resonance phenomena in periodical media and structures are investigated. The resonance phenomena are shown to occur for an unlimited discrete set of frequencies if the group velocity of the waveguide mode for them is zero; in this case, the growth of the oscillation amplitude is localized in the neighborhood of a source (localization of the resonance). A synchrophasotron resonance at which the infinite chain of oscillation sources has the oscillations phase of a corresponding traveling wave from the pass band is detected.     

Wave propagation with mass-coupling effect in fluid-saturated porous media

This article utilizes the theory of mixtures to formulate a general theory of wave propagation with mass-coupling effect in fluid-saturated porous media. An attempt is made to discuss the physical interpretation and the thermodynamic restriction of the coefficients appearing in the equations obtained. By the comparison it is shown that Biot's classical theory and the present one are essentially consistent. Also, wave velocities in some special cases are calculated, from which it is concluded that mass-coupling and permeability of media greatly affect wave propagation behavior.     

Wave propagation in an incompressible transversely isotropic fibre-reinforced elastic media

The boundary conditions at free surface of an incompressible, transversely isotropic elastic half-space are satisfied to obtain the reflection coefficients for the case when outer slowness section is re-entrant. Two quasi-shear waves will be reflected for an angular range of direction of incident wave. The numerical illustrations of reflection coefficients are presented graphically for three arbitrary materials.     

Dynamic analysis of 3-D beam elements including warping and shear deformation effects

In this paper the dynamic analysis of 3-D beam elements restrained at their edges by the most general linear torsional, transverse or longitudinal boundary conditions and subjected in arbitrarily distributed dynamic twisting, bending, transverse or longitudinal loading is presented. For the solution of the problem at hand, a boundary element method is developed for the construction of the 14 × 14 stiffness matrix and the corresponding nodal load vector of a member of an arbitrarily shaped simply or multiply connected cross section, taking into account both warping and shear deformation effects, which together with the respective mass and damping matrices lead to the formulation of the equation of motion. To account for shear deformations, the concept of shear deformation coefficients is used, defining these factors using a strain energy approach. Eight boundary value problems with respect to the variable along the bar angle of twist, to the primary warping function, to a fictitious function, to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure BEM approach that is only boundary discretization is used. Both free and forced transverse, longitudinal or torsional vibrations are considered, taking also into account effects of transverse, longitudinal, rotatory, torsional and warping inertia and damping resistance. Numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy. The influence of the warping effect especially in members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the dynamic analysis of a space frame. Moreover, the discrepancy in the dynamic analysis of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect, especially in thick walled cross section members.     

Wave propagation in porous media as a function of fluid saturation

An experimental investigation is conducted using dynamic photoelasticity and high speed photography to study the wave propagation due to blast loading in porous media as a function of fluid saturation. The porous media have been modeled as a continuous solid containing particular arrays of holes or voids. The study has focused mainly on the effect of the porous structure on transient pulse propagation as well as the effect of the moisture in the pores on wave propagation. A series of experiments have been conducted using a sheet of Homalite 100 with different geometry of the periodic array of holes. A small amount of explosive was used to generate the stress wave. Dynamic photoelastic photographs were taken with the high speed camera as the wave propagated across the holes. These data are analyzed to obtain the wave velocity as well as the stress-wave attenuation in the porous media.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Wave propagation through an interface between viscoelastic media in the presence of defects

The propagation of plane harmonic waves through an interface between viscoelastic media is considered using the equations of field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. The reflection and refraction coefficients of elastic displacement waves and the waves of a defect field characterized by a dislocation density tensor and a defect flux tensor are determined. Dependences of the obtained quantities on the parameters of the interfacing media are analyzed.     

Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory

This paper is concerned with the wave propagation behavior of rotating functionally graded(FG)temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.     

Wave propagation at interface of heat conducting micropolar solid and fluid media

The present investigation is concerned with the wave propagation at an interface of a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space. Reflection and transmission phenomena of plane waves are investigated, which impinge obliquely at the plane interface between a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space.The incident wave is assumed to be striking at the interface after propagating through the micropolar generalized thermoelastic solid. The amplitude ratios of various reflected and transmitted waves are obtained in a closed form. It is found that they are a function of the angle of incidence and frequency and are affected by the elastic properties of the media. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for a specific model. The results of some earlier literatures are also deduced from the present investigation.     

Wave propagation in inhomogeneous elastic media; normal loading of spherical and cylindrical surfaces

The propagation of waves in inhomogeneous elastic media with spherical or cylindrical symmetry, when the curved surface of the solid is given a uniform normal loading — the stress and displacement components within the solid then may be assumed to depend on one space coordinate and time alone —, is considered. The particular case in which the elastic parameters are proportional to (radius) ⁿ is considered as a special case.Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.     

Wave propagation in elastic shells

The problem of wave propagation in shells within the framework of a simplified linear shell theory is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal, transverse and bending waves. The theory is applied to wave propagation on a spherical shell.

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Résumé On traite la problème de la propagation des ondes dans les voiles minces en utilisant la méthode de Hadamard. Les vitesses de la propagation, la forme de l'onde, et aussi les effets d'accouplement sont obtenus pour les onides longitudinales, transversales et fléchissantes. On applique cette théorie à la propagation des ondes dans une coque sphérique.

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This work was supported in part by funds from the National Research Council of Canada, under Grant Number A 3805.     

Wave propagation in elastic membranes

The problem of wave propagation in linear elastic membranes is treated using the method of Hadamard. Speeds of propagation, wave shape and decay, as well as coupling effects, are obtained for longitudinal and transverse waves. Examples are considered which illustrate the features of the theory.

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Résumé On traite la problème de la propagation des ondes dans une membrane lineare et elastique, utilisant la mèthode de Hadamard. Les vitesses de la propagation, la forme del'onde, et les effets d'accouplement sont obtenus en cas des ondes longitudinales et transversales. Les exemples sont presentés qui demontrent les points essentiales de la theorie.

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This work was supported in part by funds from the National Research Council of Canada, under grant number A3805.     

Wave propagation in earth-ionosphere waveguide

Summary In this paper, wave propagation in a stratified medium which consists of earth, atmosphere and ionosphere, is studied. The ionosphere is described by a compressible plasma model where the earth magnetic field is neglected. The earth is considered as a highly conducting medium. The modal solutions due to the excitation of a vertical dipole have been obtained, where characteristic waves are analytically discussed and numerically determined.This work was supported by National Aeronautics and Space Administration under Grant NSG-395.     

Wave propagation in elastic plates

The problem of wave propagation within the framework of a complete linear theory of elastic plates is treated using the method of wave curves. A complete classification of the various extensional and bending waves is obtained, along with the corresponding speeds of propagation. These are shown to correspond to the phase velocities of harmonic waves for infinite wave number. The decay and coupling equations are found, and the problem of waves due to a punch applied to the plate surface is treated.

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Résumé On a étudié le problème de la propagation des ondes en utilisant la méthode des courbes ondiales et assumant la théorie linéaire et complète des plaques minces. On obtient une classification totale des ondes diverses, de l'extension et de la flexion, avec des vitesses de la propagation. On prouve aussi, que celles-ci correspondent avec des vitesses des phases de la propagation, en cas de nombre infinite des ondes. Les équations de la décadence et de l'accouplement sont derivées, et on a étudié le problème d'une onde, qui est produite par une emporte-pièce appliquée sur la surface d'une plaque.

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This work was supported in part by funds from the National Research Council of Canada, under Grant Number A3805.