Reflection and Transmission of Rayleigh Surface Waves by a Material Interphase

1991 ◽  
Vol 58 (3) ◽  
pp. 688-694 ◽  
Author(s):  
Z. L. Li ◽  
J. D. Achenbach
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Thin Layer ◽  
Surface Waves ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Mathematical Statement ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Rayleigh Surface Waves

Reflection and transmission of Rayleigh surface waves by a juncture normal to the free surface, between identical or different materials, has been investigated. The juncture, which may be an interface containing defects or a thin layer, is represented by a layer of extensional and shear springs. The mathematical statement of the problem is reduced to a system of singular integral equations for the displacements on the free surface and the tractions and the displacements across the juncture. Numerical solutions of this system have been computed by the use of the boundary element method. Expressions for the reflection and transmission coefficients have subsequently been obtained by the use of half-plane Green’s functions in conjunction with an elastodynamic representation integral. Results are presented for selected values of the elastic constants of the joined bodies and the stiffness parameters of the juncture.

Reflection and Transmission of a Plane Wave by an Array of Cavities in the Interface of Two Solids

1992 ◽  
Vol 59 (1) ◽  
pp. 102-108 ◽  
Author(s):  
Yonglin Xu
Keyword(s):  
Plane Wave ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Singular Integral Equations ◽  
Boundary Integral ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Typical Cell ◽  
Wave States ◽  
Doubly Periodic Array

The reflection and transmission of a plane wave by a distribution of cavities in the interface of two solids of different mechanical properties are investigated. For the calculation of the reflection and transmission coefficients by a distribution of cavities, six auxiliary wave states are used in conjunction with the reciprocal identity. Specific results are presented for scattering by a doubly periodic array of cavities in the interface of solids of different elastic moduli and mass densities. For a typical cell, the boundary integral equations for scattering by a cavity at the interface of two solids are derived on the basis of continuity of displacements and tractions across the interface and by taking advantage of the geometrical periodicity. Solutions to the system of singular integral equations have been obtained by the boundary element method. Numerical results are presented as functions of the frequency for two angles of incidence.

The acoustic signature for a surface-breaking crack produced by a point focus microscope

1992 ◽  
Vol 438 (1902) ◽  
pp. 47-65 ◽  
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Reflection And Transmission Coefficients ◽  
Reflection And Transmission ◽  
Acoustic Microscope ◽  
Transmission Coefficients ◽  
Acoustic Signature ◽  
Surface Breaking Crack ◽  
Line Focus ◽  
Fourier Integrals

The acoustic signature of a crack, breaking the surface of an otherwise homogeneous, isotropic elastic material, produced by a point focus scanning acoustic microscope is constructed theoretically. This work is patterned after a similar calculation carried out for the line focus microscope. The incident axisymmetric focused beam is constructed as a Fourier integral that produces a specified profile in the focal plane. The wavefields scattered from the specimen are also represented as Fourier integrals. Because the lens of the acoustic microscope is characterized by a large Fresnel number and an F number of order one, the Fourier integrals can be asymptotically approximated to obtain explicit expressions for the incident wavefield and for the wavefield scattered from a defect-free surface. The latter wavefield contains the leaky Rayleigh wave that is incident to the surface-breaking crack. The surface­-breaking crack is characterized by assigning it reflection and transmission coefficients. The wavefield scattered from the crack is estimated by tracing the leaky Rayleigh rays reflected and transmitted by the crack. The net wavefield scattered from the surface is then constructed by adding this crack scattered wavefield to that calculated for a defect-free surface. Lastly, the acoustic signature is calculated by using the appropriate incident and scattered wavefields in an electromechanical reciprocity identity that links the voltage measured at the microscope’s transducer to the scattered acoustic wavefields at the surface of the specimen. Expressions for acoustic signatures made using the line focus and point focus microscopes are compared. Moreover, from the expression for the acoustic signature, the Rayleigh wave reflection and transmission coefficients can be partly extracted.

Forced gravity waves in two-layered fluids with the upper fluid having a free surface

2003 ◽  
Vol 81 (4) ◽  
pp. 675-689 ◽  
Author(s):  
H H Sherief ◽  
M S Faltas ◽  
E I Saad
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Harmonic Wave ◽  
Density Ratio ◽  
Finite Depth ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Two Fluids ◽  
Lower Fluid ◽  
Wave Maker

The steady-gravity wave motion is considered for two immiscible layers of incompressible and nonviscous fluids in the presence of a porous wave maker immersed vertically in the two fluids, the upper fluid having a free surface and the lower fluid is of infinite depth. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the wave maker. Also the scattering of a harmonic wave incident normally to the wave maker is considered and the reflection and transmission coefficients are obtained. The case when the lower fluid is of finite depth is also considered. The results are plotted for different values of porosity and different values of the density ratio. PACS Nos.: 47.35.+i, 47.55.Hd, 47.55.Mh

Reflection and Transmission of Obliquely Incident Surface Waves by an Edge of a Quarter Space: Theory and Experiment

1992 ◽  
Vol 59 (2) ◽  
pp. 349-355 ◽  
Author(s):  
Z. L. Li ◽  
J. D. Achenbach ◽  
I. Komsky ◽  
Y. C. Lee
Keyword(s):  
Surface Wave ◽  
Singular Integral Equations ◽  
Angle Of Incidence ◽  
Theoretical Formulation ◽  
Reflection And Transmission ◽  
Translational Invariance ◽  
Transmission Coefficients ◽  
Obliquely Incident ◽  
Quarter Space ◽  
Definition Of

The reflection and transmission of a plane time-harmonic surface wave which is obliquely incident on the edge of a quarter space is investigated theoretically, numerically, and experimentally. The theoretical formulation of the problem, which takes advantage of the translational invariance along the edge of the quarter space, is reduced to a system of singular integral equations along axes normal to the edge, for the defracted displacement components on the faces of the quarter space axes normal to the edge. The truncation of these equations leads to the definition of reflection and transmission coefficients, R and T. The equations are solved for R, T, and the diffracted displacements by the use of the boundary element method. A self-calibrated experimental technique is proposed which deploys four surface wave transducers, and which removes the effects of variable coupling between the transducers and the faces of the quarter space as the positions of the transducers are varied. The technique is particularly suited for the measurement of |R/T| as a function of the angle of incidence. Excellent agreement is observed between numerically and experimentally obtained values.

Reflections, rays, and reverberations

1974 ◽  
Vol 64 (6) ◽  
pp. 1685-1696 ◽  
Author(s):  
B. L. N. Kennett
Keyword(s):  
Free Surface ◽  
Single Layer ◽  
Iterative Approach ◽  
Multilayered Media ◽  
Reflection And Transmission ◽  
Matrix Methods ◽  
Special Effects ◽  
Transmission Coefficients ◽  
Transmission Properties ◽  
Set Up

abstract The connection is established between conventional matrix methods for layered media and the reflection and transmission properties of a single layer. This interrelation is then used to set up an iterative approach to the calculation of reflection and transmission coefficients in multilayered media. This approach lends itself to a ray interpretation and allows estimates of errors involved in taking truncated partial ray expansions to be made. The special effects due to a free surface are also considered.

Reflection and transmission of surface waves at a vertical interface in anisotropic elastic media

1993 ◽  
Vol 83 (5) ◽  
pp. 1355-1372
Author(s):  
E. N. Its ◽  
J. S. Lee
Keyword(s):  
Surface Waves ◽  
Wave Reflection ◽  
Analytical Procedure ◽  
Far Field ◽  
Elastic Media ◽  
Reflection And Transmission ◽  
Trade Off ◽  
Transmission Coefficients ◽  
Dyadic Representation ◽  
Anisotropic Elastic

Abstract Propagation of surface waves across a vertical interface between anisotropic blocks is considered in this paper. Dyadic representation of a far field Green's function for an anisotropic half-space is constructed first. An analytical procedure is then developed to determine the reflection and transmission coefficients of surface waves at the vertical interface between two laterally homogeneous anisotropic quarter-spaces. Numerical results of Rayleigh wave reflection at vertical interfaces between dissimilar blocks are presented and the trade-off between anisotropy and inhomogeneity is discussed.

Water wave diffraction by a surface strip

2007 ◽  
Vol 571 ◽  
pp. 419-438 ◽  
Author(s):  
RUPANWITA GAYEN ◽  
B. N. MANDAL ◽  
A. CHAKRABARTI
Keyword(s):  
Integral Equations ◽  
Wave Diffraction ◽  
Water Waves ◽  
Numerical Solutions ◽  
Singular Integral Equations ◽  
Fredholm Integral Equations ◽  
Transmission Coefficients ◽  
Wide Strip ◽  
Linearized Theory ◽  
Carleman Type

The two-dimensional problem of wave diffraction by a strip of arbitrary width is investigated here in the context of linearized theory of water waves by reducing it to a pair of Carleman-type singular integral equations. These integral equations have been solved earlier by an iterative process which is valid only for a sufficiently wide strip. A new method is described here by which solutions of these integral equations are determined by solving a set of four Fredholm integral equations of the second kind, and the process is valid for a strip of arbitrary width. Numerical solutions of these Fredholm integral equations are utilized to obtain fairly accurate numerical estimates for the reflection and transmission coefficients. Previous numerical results for a wide strip are recovered from the present analysis. Additional results for the reflection coefficient are presented graphically for moderate values of the strip width which exhibit a less oscillatory nature of the curve than the case of a wide strip.

Propagation of Surface Waves Across an Anisotropic Layer

1994 ◽  
Vol 61 (3) ◽  
pp. 596-604 ◽  
Author(s):  
E. N. Its ◽  
J. S. Lee
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Differential Operators ◽  
Interface Layer ◽  
Reflection And Transmission Coefficients ◽  
Function Technique ◽  
Angle Of Incidence ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Matrix Differential

Propagation of elastic surface waves across a thin anisotropic interface layer between two vertically inhomogeneous isotropic quarter-spaces is considered. The relationship between the surface wave fields at the opposite sides of the layer is obtained in the form of matrix differential operators. Based on the Green’s function technique, an analytical method is developed to calculate reflection and transmission coefficients of Rayleigh waves at the layer. The reflection and transmission coefficients of Rayleigh waves at the interface layer are calculated as a function of the angle of incidence for various models of layers with hexagonal symmetry and results are discussed in some detail. Several isotropic layers of low or high velocity materials are also considered to examine the trade-off between anisotropy and inhomogeneity of the interface layer.

Similarity solution for oblique water entry of an expanding paraboloid

2014 ◽  
Vol 745 ◽  
pp. 398-408 ◽  
Author(s):  
G. X. Wu ◽  
S. L. Sun
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Nonlinear Boundary ◽  
Velocity Potential ◽  
Numerical Solutions ◽  
Nonlinear Boundary Conditions ◽  
Water Entry ◽  
Similarity Solutions ◽  
Pressure Distributions ◽  
Flow Features

AbstractSimilarity solutions based on velocity potential theory are found to be possible in the case of an expanding paraboloid entering water when gravity is ignored. Numerical solutions are obtained based on the boundary element method. Iteration is used for the nonlinear boundary conditions on the unknown free surface, together with regular remeshing. Results are obtained for paraboloids with different slenderness (or bluntness). Flow features and pressure distributions are discussed along with the physical implications. It is also concluded that similarity solutions may be possible in more general cases.

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