The effect of boundaries on wave propagation in a liquid-filled porous solid: V. Transmission across a plane interface

1964 ◽  
Vol 54 (1) ◽  
pp. 409-416
Author(s):  
H. Deresiewicz ◽  
J. T. Rice
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Body Waves ◽  
Porous Solid ◽  
Plane Interface ◽  
Plane Body ◽  
Cross Sectional ◽  
Material Constants ◽  
Transmitted Waves

abstract The passage of plane body waves across a plane interface from one to another, contiguous, porous aggregate is examined, with particular attention paid to motions involving wave lengths large in comparison with cross-sectional pore dimensions. The results are obtained for a rather general set of boundary conditions which take account of possible resistance to flow due to partial nonalignment of pores at the interface. It is found that when certain conditions of equality of material constants for the two media are met one or more of the reflected and transmitted waves are extinguished.

The effect of boundaries on wave propagation in a liquid-filled porous solid

1960 ◽  
Vol 50 (4) ◽  
pp. 599-607
Author(s):  
H. Deresiewicz
Keyword(s):  
Wave Propagation ◽  
Free Boundary ◽  
General Solution ◽  
Elastic Waves ◽  
Body Waves ◽  
Porous Solid ◽  
Field Equations ◽  
Reflected Waves ◽  
Three Body ◽  
Propagation Of Elastic Waves

ABSTRACT A general solution is deduced of the differential equations which describe the propagation of elastic waves in a nondissipative liquid-filled porous solid. The solution is then used to examine some of the phenomena which arise when each of the three body waves predicted by the field equations is, in turn, incident on a plane traction-free boundary. It is found, for example, that an obliquely incident wave of each type in general gives rise to reflected waves of all three types.

Reflection and Refraction of Waves at a Planar Composite Interface

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Wave Propagation ◽  
Composite Materials ◽  
Boundary Conditions ◽  
Practical Importance ◽  
Ultrasonic Waves ◽  
Plane Interface ◽  
Contact Method ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Composite Interface

Nondestructive ultrasonic testing of composite materials is affected by several special features of wave propagation that arise from the strong anisotropy and inhomogeneity of these materials. The resulting complexity requires re-examination of old testing methodologies and development of new ones. One of the most fundamental phenomena in ultrasonic nondestructive evaluation is the reflection–refraction of ultrasonic waves at a plane interface. Even the simplest test procedure requires understanding of mode conversion and knowledge of elastic wave reflection and transmission coefficients and refraction angles. Reflection–refraction phenomena, while straightforward and well documented for isotropic materials, are much more complicated for anisotropic materials. When analyzing the oblique incidence inspection method for composite materials, one first has to address the problem of wave propagation through the interface between the coupling medium and the composite material. For example, there is an inherent fluid/composite interface in the immersion technique and a perspex/composite interface in the contact method. In the latter case, assuming that a thin fluid layer is applied to facilitate coupling through the interface, slip rather than welded boundary conditions prevail. Another example of great practical importance is the case of multidirectional fiber plies in a composite laminate, when the reflection and transmission of ultrasonic waves from one ply to another with a different orientation must be considered. Before discussing the general problem of wave refraction in anisotropic composite materials, let us review the simple isotropic case. Consider a plane interface between two isotropic elastic media in “welded” (perfectly bonded) contact, implying continuity of tractions and displacements across the interface, although the boundary conditions are not important at this point. Figure 4.1 shows a schematic diagram of a plane wave with wavenumber ki incident on the interface at angle θi. The parallel lines with spacing equal to the incident wavelength λi correspond to equal-phase planes orthogonal to the incident plane. By definition, the wavenumber ki = 2π/λi is the magnitude of the wave vector ki. The incident wave is converted at the interface into reflected and transmitted waves. The refraction angle of the transmitted wave is θr and its wavenumber is kr.

Wave propagation in electro‐magneto‐elastic solid plate of polygonal cross‐sections

2013 ◽  
Vol 9 (1) ◽  
pp. 23-48 ◽  
Author(s):  
P. Ponnusamy
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Cross Sections ◽  
Elastic Plate ◽  
Elastic Solid ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Cross Sectional ◽  
Content Type ◽  
Solid Plate

PurposeThis paper aims to describe the method for solving vibration problem of electro‐magneto‐elastic plate of polygonal (triangle, square, pentagon and hexagon) cross‐sections using Fourier expansion collocation method (FECM).Design/methodology/approachA mathematical model is developed to study the wave propagation in an electro‐magneto‐elastic plate of polygonal cross‐sections using the theory of elasticity. The frequency equations are obtained from the arbitrary cross‐sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the surface of the plate directly. Hence, the FECM is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.FindingsFrom the literature survey, it is clear that the free vibration of electro‐magneto‐elastic plate of polygonal cross‐sections have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of electro‐magneto‐elastic plates are based on the traditional circular cross‐sections only. So, in this paper, the wave propagation in electro‐magneto‐elastic plate of polygonal cross‐sections is studied using the FECM. The computed non‐dimensional frequencies are plotted in the form of dispersion curves and their characteristics are discussed.Originality/valueThe researchers have discussed the circular, rectangular, triangular and square cross‐sectional plates by the boundary conditions. In this problem, the author studied the vibrations of polygonal (triangle, square, pentagon and hexagon) cross‐sectional plates using the geometrical relation which is applicable to all the cross‐sections. The problem may be extended to any kinds of cross‐sections by using the proper geometrical relations.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Period equation for Rayleigh waves in a layer overlying a half space with a sinusoidal interface

1962 ◽  
Vol 52 (4) ◽  
pp. 807-822 ◽  
Author(s):  
John T. Kuo ◽  
John E. Nafe
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Length ◽  
Linear Equations ◽  
Wave Number ◽  
Interface Plane ◽  
Period Equation ◽  
Phase And Group Velocities

abstract The problem of the Rayleigh wave propagation in a solid layer overlying a solid half space separated by a sinusoidal interface is investigated. The amplitude of the interface is assumed to be small in comparison to the average thickness of the layer or the wave length of the interface. Either by applying Rayleigh's approximate method or by perturbating the boundary conditions at the sinusoidal interface, plane wave solutions for the equations which satisfy the given boundary conditions are found to form a system of linear equations. These equations may be expressed in a determinant form. The period (or characteristic) equations for the first and second approximation of the wave number k are obtained. The phase and group velocities of Rayleigh waves in the present case depend upon both frequency and distance. At a given point on the surface, there is a local phase and local group velocity of Rayleigh waves that is independent of the direction of wave propagation.

Reflection and transmission of elastic waves in a system of corrugated layers

1967 ◽  
Vol 57 (3) ◽  
pp. 393-419
Author(s):  
A. Levy ◽  
H. Deresiewicz
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Scattered Field ◽  
Single Layer ◽  
Body Waves ◽  
Numerical Computations ◽  
Plane Body ◽  
Reflection And Transmission ◽  
Plane Parallel

abstract The scattered field generated by normally incident body waves in a system of layers having small, but otherwise arbitrary, periodic deviations from plane parallel boundaries is shown to consist of superposed plane body and surfacetype waves. Results of numerical computations for two like half-spaces separated by a sinusoidally corrugated single layer, and by two layers, reveal the variation of the amplitude of the field with ratios of velocities, densities, impedances, and with those of depth of layers and wavelength of the boundary corrugations to the wavelength of the incident wave.

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