Reflection Of Plane Elastic Waves Research Articles

Rotation Effect on Reflection of Plane Elastic Waves at a Free Surface Under Initial Stress, Magnetic Field and Temperature Field

Rotation Effect on Reflection of Plane Elastic Waves at a Free Surface Under Initial Stress, Magnetic Field and Temperature Field

Effect of local fluid flow on reflection of plane elastic waves at the boundary of a double-porosity medium

This study solves a mathematical model for the propagation of harmonic plane waves in a double-porosity solid saturated by a viscous fluid. An eigen-system of order four implies the existence of three longitudinal waves and a transverse wave in the composite porous medium. Eigenvalues of this system define the four complex velocities, which are resolved further to define the phase velocities of four attenuated waves in the medium. Variation of the fluid content in pores due to the wave-induced flow is expressed in terms of dilatations of the constituents in porous aggregate. Reflection of plane waves is studied at the stress-free plane surface of the medium. A numerical example is solved to calculate the partition of the incident energy among the four reflected waves. Conservation of the incident energy flux at the boundary is obtained through the presence of an interaction energy share, even when the poroelastic solid is saturated with a non-viscid fluid. This interaction energy disappears in the absence of the wave-induced flow in non-dissipative porous medium. Else, this interaction energy represents the net dissipation effect of the wave-induced flow as well as the pore-fluid viscosity on the partition of the incident energy at the free surface.

Reflection of plane elastic waves in tetragonal crystals with strong anisotropy

Propagation and reflection of plane elastic waves in the acousto-optic crystals tellurium dioxide, rutile, barium titanate, and mercury halides are examined in the paper. The reflection from a free and flat boundary separating the crystals and the vacuum is investigated in the (001) planes in the case of glancing acoustic incidence on the boundary. The analysis shows that two bulk elastic waves may be reflected from the crystal surface. The energy flow of one of the reflected waves in paratellurite and in the mercury compounds propagates in a quasi-back-direction with respect to the incident energy flow. It is proved that energy flows of the incident and reflected elastic waves are separated by a narrow angle of only a few degrees. It is also found that the relative intensity of the unusually reflected waves is close to a unit in a wide variety of crystal cuts. General conclusions related to acoustic propagation and reflection in crystals have been made based on the examined phenomena in the materials.

Influence of Strong Acoustic Anisotropy on Reflection of Bulk Acoustic Waves in Crystals

Propagation and reflection of plane elastic waves in the acousto-optic crystals tellurium dioxide and calomel as well as in the ferroelectric material barium titanate is examined in the paper. The reflection of the waves from a free and flat boundary separating the crystal and the vacuum is investigated in the (001) planes of TeO2, Hg2Cl2 and BaTiO3 in the case of glancing acoustic incidence on the boundary. The analysis shows that as much as two elastic waves may be reflected from the crystal surface. Energy flow of one of the reflected waves in paratellurite and calomel propagates in a quasi-back direction with respect to the incident energy flow so that both energy flows are separated by an angle as narrow as a few degrees. It is found that a relative intensity of the unusually reflected wave in the acousto-optic crystals may be close to a unit in a wide variety of crystal cuts. Possible applications of the examined phenomena in acousto-optic devices are discussed in the presentation.

Transformation of Acoustic Modes in Case of Arbitrary Reflection in Acousto-Optic Crystals

The phenomenon of unusual reflection of plane elastic waves is examined in the crystalline compounds of tellurium and mercury. It is predicted and registered in experiments that energy flow of one of the reflected waves may propagate practically in a back direction with respect to an incident energy flow. This phenomenon is observed in the materials with a strong anisotropy of elastic properties. In the case of inclined incidence, the reflection may take place strictly in the back direction with respect to the intrinsic energy flow. Moreover, all incident elastic energy may be reflected in a form of a back elastic wave. The analysis was carried out for all exisiting cases of inclined incidence in the crystals. It was proved that relative intensity of the unusually reflected wave might be close to a unit in a wide variety of incidence and cut angles in the crystals. A comparative analysis of the effect in new anisotropic materials and in the well-known crystals has been carried out. Since the crystals under investigation possess relatively high magnitudes of acousto-optic figure of merit, e.g. paratellurite and calomel, principal results of the research are of significance in development of new generations of acousto-optic devices.

A reflection/transmission matrix formulation for seismoacoustic scattering by an irregular fluid--solid interface

The seismoacoustic scattering due to an irregular fluid—solid interface (i.e. the ocean bottom) must be considered when modelling seismic wave propagation in oceanic regions. In this paper, we present an accurate method to treat this problem. The method is an extension of the reflection/transmission matrix approach that was developed to model scattering due to an irregular interface between two elastic solids. This approach uses the discrete wavenumber representation of the wavefield and the Rayleigh ansatz; the wavefield is decomposed into a set of plane waves, and we assume that the scattered wavefield due to an incident plane wave can be expanded in terms of only the waves moving away from the interface. The plane waves at both sides of the interface are then connected to each other based on this hypothesis and proper boundary conditions. The elements of the reflection/transmission matrices describe these connection coefficients. As the fluid—solid interface, the direct application of the above method is difficult because the tangential displacement at the interface is not necessarily continuous. To avoid this problem, we use pressure as the variable inside the fluid layer. The reflection/transmission matrices between the pressure wave (i.e. the acoustic wave) and the elastic waves are then developed by using the standard boundary conditions at the fluid—solid interface (i.e. normal stress continuity, zero tangential stress, and normal displacement continuity) and the Rayleigh ansatz. To demonstrate the validity and feasibility of our method, we compare the results of our method with those of other methods. First, we examine the reflection of plane elastic waves by a periodic sinusoidal interface for a single frequency. The interface profile is characterized by its periodicity or wavelength (D) and peak to trough height (h). The behaviour of the reflection calculated by our method shows almost complete agreement with that calculated by a boundary element method (BEM) up to a relatively steep interface whose height to wavelength ratio (h/D) is 0.5. Second, we calculate the synthetic time domain waveforms for a plane vertically incident P wave into basin-like fluid layers. We compare the waveforms calculated by the present method with those calculated by the finite difference method (FDM). In general, the waveforms calculated by the two methods match well. A quantitative study shows that the degree of agreement indicated by the RMS residuals between the waveforms of the two methods becomes better when we use a smaller grid interval in the FDM calculation. For the models treated here, the cases of 30 grid-points per wavelength results in RMS residuals less than about 10–15 per cent. This grid interval is smaller than that usually applied (more than 5–10 grid-points per wavelength). Since, in general, the accuracy of the FDM calculation becomes better as the grid interval decreases, these results indicate the validity of the present method.

Elastic waves in monoclinic incompressible materials and reflection from an interface

The reflection of plane elastic waves from a free surface of monoclinic incompressible materials is examined under plane strain conditions in a plane of material symmetry. It is found that this problem can be equivalently treated by elastic wave reflection in orthotropic incompressible materials if the material constants of the monoclinic material are properly related to those of the orthotropic material. Thus the range of existence of the two (one homogeneous and the other homogeneous or inhomogeneous) reflected waves in a monoclinic material, including points corresponding to zero amplitude reflected waves, can be obtained from that given in a previous paper [Nair and Sotiropoulos, J. Acoust. Soc. Am. 102, 102–109 (1997)] where an orthotropic material was treated.

On the reflection of elastic waves in monoclinic incompressible materials.

The reflection of plane elastic waves from a free surface of monoclinic incompressible materials is examined under plane strain conditions in a plane of material symmetry. The propagation condition is derived which together with the law of reflection yields an inequality that defines the range of existence of the two (one homogeneous and the other homogeneous or inhomogeneous) reflected waves in terms of the angle of incidence of a homogeneous wave, the orientation of the free‐surface with respect to a material axis of symmetry, and the elastic constants of the monoclinic material. The critical orientation beyond which there exist two homogeneous reflected waves is derived in explicit form in terms of the elastic constants. One of these reflected waves has an angle of reflection equal to the angle of incidence only for specific orientations which are found. In the range of existence of the two reflected waves, exclusion points are defined for which there exists only one reflected (homogeneous) wave with nonzero amplitude.

Energy Reflection of Elastic Waves from an Inhomogeneous Layer.

Energy reflection of plane elastic waves impinging on an inhomogeneous elastic layer is investigated. The variation of acoustic impedance throughout the inhomogeneous layer is given as a linear function of thickness coordinate of the layer. Closed-form analytical solutions of the coefficient of energy reflection and transmission are obtained for the normal case to show fundamental but reliable results. The discontinuity of acoustic impedance at interfaces dominantly affects energy reflection. The effect is systematically explained from the variation in impedance. The special coefficients for the long wave limit coincide with the well-known results for a homogeneous elastic layer. The model presented here may be applicable to such materials as a transitional layer of deteriorated bonding interface or a layer of functionally gradient material.

Reflection of plane waves under initial stresses at a free surface

The paper deals with the phenomenon of reflection of plane elastic waves in a free surface when the medium is initially stressed. It has been shown analytically that the reflected P and SV waves depend on initial stresses present in the medium. The numerical values of reflection coefficients for different initial stresses and the angle of incidence have been calculated by the Computer I.C.L. 1901-A and the results are given in the form of graphs. Many interesting results are found in the paper which are not seen in an initially stress-free medium.

Errata to reflection of plane elastic waves from transition layers with arbitrary variation of velocity and density

Errata to reflection of plane elastic waves from transition layers with arbitrary variation of velocity and density

Reflection of plane elastic waves from transition layers with arbitrary varration of velocity and density

abstract The problem of reflection of plane elastic waves is generalized numerically to an arbitrary variation, with depth, of the elastic parameters inside a transition layer between two homogeneous half-spaces. Numerical results are given for some cases of interest.

A Note on the Refraction and Reflection of Plane Elastic Waves at an Interface With a Large Velocity Contrast

Research Article| December 01, 1958 A Note on the Refraction and Reflection of Plane Elastic Waves at an Interface With a Large Velocity Contrast Otto W. Nuttli Otto W. Nuttli Search for other works by this author on: GSW Google Scholar Author and Article Information Otto W. Nuttli Publisher: Seismological Society of America First Online: 03 Mar 2017 Online Issn: 1938-2057 Print Issn: 0895-0695 © 1958 by the Seismological Society of America Seismological Research Letters (1958) 29 (4): 45–46. https://doi.org/10.1785/gssrl.29.4.45 Article history First Online: 03 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Otto W. Nuttli; A Note on the Refraction and Reflection of Plane Elastic Waves at an Interface With a Large Velocity Contrast. Seismological Research Letters 1958;; 29 (4): 45–46. doi: https://doi.org/10.1785/gssrl.29.4.45 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietySeismological Research Letters Search Advanced Search This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.