Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

Wave reflection and refraction in layered media is a topic closely related to seismology,acoustics,geophysics and earthquake engineering.Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials.The system is composed of ideal fluid,porous medium,and underlying elastic solid.By numerical examples,the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed.The results show that the existence of the porous medium,especially in the partially saturated case,may significantly affect the dynamic pressures of the overlying fluid.

A possible mechanism of current in medium under electromagnetic wave

In this paper a possible mechanism of current in medium is presented. Comparison between this current and the magnetization current was made. Expression for this current was derived. This work is helpful to understanding the interaction between medium and electromagnetic wave.

Propagation of acoustic wave in viscoelastic medium permeated with air bubbles

Based on the modification of the radial pulsation equation of an individual bubble, an effective medium method （EMM） is presented for studying propagation of linear and nonlinear longitudinal acoustic waves in viscoelastic medium permeated with air bubbles. A classical theory developed previously by Gaunaurd （Gaunaurd GC and UEberall H, J. Acoust, Soc, Am., 1978; 63： 1699-1711） is employed to verify the EMM under linear approximation by comparing the dynamic （i.e. frequency-dependent） effective parameters, and an excellent agreement is obtained. The propagation of longitudinal waves is hereby studied in detail, The results illustrate that the nonlinear pulsation of bubbles serves as the source of second harmonic wave and the sound energy has the tendency to be transferred to second harmonic wave, Therefore the sound attenuation and acoustic nonlinearity of the viscoelastic matrix are remarkably enhanced due to the system＇s resonance induced by the existence of bubbles.

ON THE INTERACTION OF WATER WAVES AND SEABED BY THE POROUS MEDIUM MODEL

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results.

Propagation of plane P-waves at interface between elastic solid and unsaturated poroelastic medium

A linear viscoporoelastic model is developed to describe the problem of reflection and transmission of an obliquely incident plane P-wave at the interface between an elastic solid and an unsaturated poroelastic medium, in which the solid matrix is filled with two weakly coupled fluids （liquid and gas）. The expressions for the amplitude reflection coefficients and the amplitude transmission coefficients are derived by using the potential method. The present derivation is subsequently applied to study the energy conversions among the incident, reflected, and transmitted wave modes. It is found that the reflection and transmission coefficients in the forms of amplitude ratios and energy ratios are functions of the incident angle, the liquid saturation, the frequency of the incident wave, and the elastic constants of the upper and lower media. Numerical results are presented graphically. The effects of the incident angle, the frequency, and the liquid saturation on the amplitude and the energy reflection and transmission coefficients are discussed. It is verified that in the transmission process, there is no energy dissipation at the interface.

WAVE FIELD EXTRAPOLATION IN VISCOELASTIC MEDIUM AND VARIABLE FOCUS METHOD TO SEPARATE SEISMIC COMPOUND WAVE

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Reflection of Plane Waves from a Free Surface of an Initially Stressed Transversely Isotropic Dissipative Medium

The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the speeds of plane waves. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflection coefficients of reflected quasi-P (qP) and quasi-SV (qSV) waves in closed form for the incidence of qP and qSV waves. A particular model is chosen for numerical computation of these reflection coefficients for a certain range of the angle of incidence. The numerical values of these reflection coefficients are shown graphically against the angle of incidence for different values of initial stress parameter. The impact of initial stress parameter on the reflection coefficients is observed significantly.

Borehole guided waves in a non-Newtonian(Maxwell) fluid-saturated porous medium

The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot＇s theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.

Study on Propagation Characteristics of Plasma Surface Wave in Medium Tube

Axial propagation characteristics of the axisymmetric surface wave along the plasma in the medium tube were studied. The expressions of electromagnetic field inside and outside the medium tube were deduced. Also, the impacts of several factors, such as plasma density, signal frequency, inner radius of medium tube, collision frequency, etc., on plasma surface wave propa- gation were numerically simulated. The results show that, the properties of plasma with higher density and lower gas pressure are closer to those of metal conductor. Furthermore, larger radius of medium tube and lower signal frequency are better for surface wave propagation. However, the effect of collision frequency is not obvious. The optimized experimental parameters can be chosen as the plasma density of about 10^17 m^-3 and the medium radius between 11 mm and 19 mm.

LINEAR THEORY OF GRAVITY WAVES ON A VOIGT VISCOELASTIC MEDIUM

Linear surface gravity waves on a semi-infinite incompressible Voigt medium are studied in this paper.Three dimensionless parameters,the dimensionless viscoelastic parameter (?),the dimensionless wave number and the dimensionless sur- face tension are introduced.A dimensionless characteristic equation describing the waves is derived.This is a sixth order complex algebraic equation which is solved to give the complex dispersion relation.Based on the numerical solution, two critical values of (?),(?)_A=0.607 and (?)_R=2.380,which represent the appearance of the cutoff region and the disappearance of the strong dispersion region,are found.The effects of (?) on the characteristic equation and the properties of the waves are discussed.

Reflection of thermoelastic wave on the interface of isotropic half-space and tetragonal syngony anisotropic medium of classes 4, 4/m with thermomechanical effect

The thermoelastic wave propagation in a tetragonal syngony anisotropic medium of classes 4, 4/m having heterogeneity along z axis has been investigated by employing matrizant method. This medium has an axis of second-order symmetry parallel to z axis. In the case of the fourth-order matrix coefficients, the problems of wave refraction and reflection on the interface of homogeneous anisotropic thermoelastic mediums are solved analytically.

Reflection for three-dimensional plane waves in triclinic crystalline medium

The propagation of three-dimensional plane waves at a traction free boundary of a half-space composed of triclinic crystalline material is discussed. A method has been developed to find the analytical expressions of all the three phase velocities of quasi-P （qP）, quasi-SV （qSV） and quasi-SH （qSH） in three dimensions. Closed form expressions in three dimensions for the amplitude ratios of reflection coefficients of qP, qSV and qSH waves in a triclinic medium are obtained. These expressions are used for numerically studying the variation of the reflection coetticients with the angle of incidence. The graphs are drawn for different polar angle and azimuth. Numerical results presented indicate that the anisotropy affect the reflection coetticients significantly in the three dimensional case compared to the two-dimensional case.

Feedback control of wave segments in an excitable medium

Depending on the excitability of the medium, a propagating wave segment will either contract or expand to fill the medium with spiral waves. This paper aims to introduce a simple mechanism of feedback control to stabilize such an expansion or contraction. To do this, we lay out a feedback control system in a block diagram and reduce it into a bare, universal formula. Analytical and experimental findings are compared through a series of numerical simulations of the Barkley model.

Mathematical Modeling and Analysis of Torsional Surface Waves in a Transverse Isotropic Elastic Solid Semi-Infinite Medium with Varying Rigidity and Density under a Rigid Layer

In this paper, mathematical modeling of the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density under a rigid layer has been considered. The equation of motion has been formulated in the elastic medium using suitable boundary conditions. The frequency equation containing Whittaker’s function for phase velocity due to torsional surface waves has been derived. The effect of rigid layer in the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density has been discussed. The numerical results have been shown graphically. It is observed that the influence of transverse and longitudinal rigidity and density of the medium have a remarkable effect on the propagation of the torsional surface waves. Frequency equations have also been derived for some particular cases, which are in perfect agreement with some standard results.

Study on the Physical Basis of Wave-Particle Duality: Modelling the Vacuum as a Continuous Mechanical Medium

One great surprise discovered in modern physics is that all elementary particles exhibit the property of wave-particle duality. We investigated this problem recently and found a simple way to explain this puzzle. We proposed that all particles, including massless particles such as photon and massive particles such as electron, can be treated as excitation waves in the vacuum, which behaves like a physical medium. Using such a model, the phenomenon of wave-particle duality can be explained naturally. The key question now is to find out what kind of physical properties this vacuum medium may have. In this paper, we investigate if the vacuum can be modeled as an elastic solid or a dielectric medium as envisioned in the Maxwell theory of electricity and magnetism. We show that a similar form of wave equation can be derived in three cases: (1) By modelling the vacuum medium as an elastic solid;(2) By constructing a simple Lagrangian density that is a 3-D extension of a stretched string or a vibrating membrane;(3) By assuming that the vacuum is a dielectric medium, from which the wave equation can be derived directly from Maxwell’s equations. Similarity between results of these three systems suggests that the vacuum can be modelled as a mechanical continuum, and the excitation wave in the vacuum behaves like some of the excitation waves in a physical medium.

On Propagation of Rayleigh Type Surface Wave in a Micropolar Piezoelectric Medium

In the present paper, the governing equations of a linear transversely isotropic micropolar piezoelectric medium are specialized for x-z plane after using symmetry relations in constitutive coefficients. These equations are solved for the general surface wave solutions in the medium. Following radiation conditions in the half-space, the particular solutions are obtained, which satisfy the appropriate boundary conditions at the stress-free surface of the half-space. A secular equation for Rayleigh type surface wave is obtained. An iteration method is applied to compute the non-dimensional wave speed of the Rayleigh surface wave for specific material parameters. The effects of piezoelectricity, non-dimensional frequency and non-dimensional material constant, charge free surface and electrically shorted surface are shown graphically on the wave speed of Rayleigh wave.

SOME PROPERTIES OF FAR FIELD PATTERNS OF ACOUSTIC WAVES IN AN INHOMOGENEOUS MEDIUM

In this paper, by using functional analysis and integral equation method, we obtain some results about the properties of far field of acoustic waves in an inhomogeneous medium. And we also discuss some ill-posed inverse scattering problems by Tikhonov regularization method.

P-wave velocity prediction in porous medium with liquid-pocket patchy saturation

It becomes increasingly clear that non-uniform distribution of immiscible fluids in porous rock is particularly relevant to seismic wave dispersion. White proposed a patchy saturation model in 1975, in which spherical gas pockets were located at the center of a liquid saturated cube. For an extremely light and compressible inner gas, the physical properties can be approximated by a vacuum with White＇s model. The model successfully analyzes the dispersion phenomena of a P-wave velocity in gas-water- saturated rocks. In the case of liquid pocket saturation, e.g., an oil-pocket surrounded by a water saturated host matrix, the light fluid-pocket assumption is doubtful, and few works have been reported in White＇s framework. In this work, Poisson＇s ratio, the bulk modulus, and the effective density of a dual-liquid saturated medium are formulated for the heterogeneous porous rocks containing liquid-pockets. The analysis of the difference between the newly derived bulk modulus and that of White＇s model shows that the effects of liquid-pocket saturation do not disappear unless the porosity approaches zero. The inner pocket fluid can no longer be ignored. The improvements of the P-wave velocity predictions are illustrated with two examples taken from experiments, i.e., the P-wave velocity in the sandstone saturated by oil and brine and the P-wave velocity for heavy oils and stones at different temperatures.

Blast Waves in Multi-Component Medium with Thermal Relaxation

The mathematical models of relaxing media with a structure for describing nonlinear long-wave processes are explored. The wave processes in non-equilibrium heterogeneous media are studied in terms of the suggested asymptotic averaged model. On the microstructure level of the medium, the dynamical behavior is governed only by the laws of thermodynamics, while, on the macrolevel, the motion of the medium can be described by the wave-dynamical laws. It is proved rigorously that on the acoustic level, the propagation of long waves can be properly described only in terms of dispersive dissipative properties of the medium, and in this case, the dynamical behavior of the medium can be modeled by a homogeneous relaxing medium. At the same time, the dynamical behavior of the medium cannot be modeled by a homogeneous medium even for long waves, if they are nonlinear. For a finite-amplitude wave, the structure of medium produces nonlinear effects even if the individual components of the medium are described by a linear law. The heterogeneity of the structure of medium always introduces additional nonlinearity. It is shown that the solution of many problems for multi-component media with incompressible phases can be obtained through the known solution of a similar problem for a homogeneous compressible medium by means of the suggested transformation. It is not necessary to solve directly the problem for the medium with incompressible component, and it is sufficient just to transform the known solution of the similar problem for a homogeneous medium. The scope for the suggested transformation is demonstrated by the reference to the strong explosion state in a two-phase medium. The special attention is focused on the research of blast waves in multi-component media with thermal relaxation. The dependence of the shock damping parameters on the thermal relaxation time is analyzed in order to provide a deeper understanding of the damping of shock waves in such media and to determine their effectiveness as localizing media. This problem attracts the interest also in view of the practical possibility to estimate the efficiency of medium for damping the shock wave action. To find the nature of the relaxation interaction between the components of medium and to estimate the attenuation of shock waves generated by solid explosives, we have studied experimentally both the velocity field of shock waves and the pressure at front in an air foam. The comparison of experimental and theoretical investigations of the relaxation phenomena which accompany the propagation of shock waves in foam indicates that within the scope of relaxation hydrodynamics it is possible to explain the observed phenomena and estimate the efficiency of medium as localizer of the shock wave action.

Mathematical framework of nonlinear elastic waves propagating in pre-stressed media

Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.