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

1966 ◽  
Vol 56 (3) ◽  
pp. 633-642 ◽  
Author(s):  
Ravindra N. Gupta
Keyword(s):  
Transition Layer ◽  
Elastic Waves ◽  
Numerical Results ◽  
Elastic Parameters ◽  
Transition Layers

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.

Parameterization of Eddy Fluxes near Oceanic Boundaries

2008 ◽  
Vol 21 (12) ◽  
pp. 2770-2789 ◽  
Author(s):  
Raffaele Ferrari ◽  
James C. McWilliams ◽  
Vittorio M. Canuto ◽  
Mikhail Dubovikov
Keyword(s):  
Boundary Layer ◽  
Transition Layer ◽  
General Circulation ◽  
Mesoscale Eddies ◽  
Turbulent Boundary Layers ◽  
Mesoscale Variability ◽  
Transition Layers ◽  
Boundary Layer Turbulence ◽  
Dynamical Coupling ◽  
Eddy Fluxes

Abstract In the stably stratified interior of the ocean, mesoscale eddies transport materials by quasi-adiabatic isopycnal stirring. Resolving or parameterizing these effects is important for modeling the oceanic general circulation and climate. Near the bottom and near the surface, however, microscale boundary layer turbulence overcomes the adiabatic, isopycnal constraints for the mesoscale transport. In this paper a formalism is presented for representing this transition from adiabatic, isopycnally oriented mesoscale fluxes in the interior to the diabatic, along-boundary mesoscale fluxes near the boundaries. A simple parameterization form is proposed that illustrates its consequences in an idealized flow. The transition is not confined to the turbulent boundary layers, but extends into the partially diabatic transition layers on their interiorward edge. A transition layer occurs because of the mesoscale variability in the boundary layer and the associated mesoscale–microscale dynamical coupling.

Nonlinear Elastic Waves in a 1D Layered Composite Material: Some Numerical Results

2011 ◽  
Author(s):  
Igor Andrianov ◽  
Vladislav Danishevs’kyy ◽  
Dieter Weichert ◽  
Heiko Topol ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Composite Material ◽  
Elastic Waves ◽  
Layered Composite ◽  
Numerical Results ◽  
Layered Composite Material ◽  
Nonlinear Elastic

Reflection and Transmission by a Periodic Array of Coplanar Cracks: Normal and Oblique Incidence

1993 ◽  
Vol 60 (4) ◽  
pp. 911-919 ◽  
Author(s):  
Yozo Mikata
Keyword(s):  
Elastic Waves ◽  
Oblique Incidence ◽  
Numerical Results ◽  
Periodic Array ◽  
Fourier Series Expansion ◽  
Periodic Case ◽  
Single Crack ◽  
Reflection And Transmission ◽  
Numerical Integrations ◽  
Coplanar Cracks

Scattering of in-plane elastic waves by a periodic array of coplanar cracks is investigated. This problem was first treated by Angel and Achenbach. The method of their solution was based on the Fourier series expansion of the Green-Lame potentials. In this paper, we have extended van der Hijden and Neerhoff’s treatment of scattering of in-plane elastic waves by a single crack to the periodic case. Major advantages of our treatment over Angel and Achenbach are: (1) the formulation is relatively simple, straightforward, and unified for both normal and oblique incidence, and (2) more importantly, there is no need for numerical integrations, because all the integrations involved in the formulation can be analytically evaluated thanks to the periodicity of the problem and the coplanarity of the cracks. Numerical results are presented and compared with those of Angel and Achenbach. Some new numerical results are also presented.

scholarly journals Effect of Transition Layer on Properties of Tungsten-Tantalum (W-Ta) Laminated Composite

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 558
Author(s):  
Zizhi Yan ◽  
Gaoyong Xu ◽  
Jinping Suo
Keyword(s):  
Transition Layer ◽  
Laminated Composites ◽  
Laminated Composite ◽  
High Strength ◽  
Fracture Morphology ◽  
Bending Test ◽  
Tensile Fracture ◽  
Transition Layers ◽  
Three Point Bending ◽  
Plasma Sintering

Tungsten has many attractive properties, but its brittleness limits its application. Our team has found that the brittleness of tungsten can be greatly improved by combining the brittle tungsten with tantalum. Furthermore, we found that if a suitable transition layer is added between tungsten and tantalum, the properties of the composite will be further improved. In this paper, we studied the effect of different transition layers on the properties of W-Ta laminated composite to explore a suitable transition layer, which can effectively improve the toughness of the composite and solve the problem of tungsten application. We have prepared four kinds of W-Ta laminated composites with Ni, Ti, Nb, and Mo as transition layers. Ta-W laminated composites were prepared by stacking layers with Ta, transition layer, W alternately and sintered by spark plasma sintering (SPS). The tensile and three-point bending tests were carried to compare the mechanical properties. The tensile fracture morphology and three-point bending crack distribution were observed by SEM. In addition, the diffusion of elements in the transition layer and the influence of element diffusion on the tungsten structure were also studied to clarify the toughening mechanism. The results show that Nb is a satisfying transition layer, which not only improves the strength of W-Ta laminated composite, but also improves the toughness. The tensile test of W/Nb/Ta laminated composite shows a typical plastic fracture mode with an elongation of 13%. Three-point bending test also shows high strength and good toughness. In addition, Voigt model was used to predict the elastic modulus of W-Ta laminated composites and compared with the experimental results.

Reflection of elastic waves from a linear transition layer

1966 ◽  
Vol 56 (2) ◽  
pp. 511-526
Author(s):  
Ravindra N. Gupta
Keyword(s):  
Plane Wave ◽  
Material Properties ◽  
Transition Layer ◽  
Elastic Waves ◽  
Wave Reflection ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Arbitrary Angle ◽  
S Wave ◽  
Incidence Plane

abstract A separation of P- and S-wave potentials is achieved for an inhomogeneous medium in which density is constant and Lame's parameters, λ and μ, are assumed to vary as λ/λ1 = μ/μ1 = (1 + bz)2 where λ1, μ1 and b are constants. The resulting equations are solved for an arbitrary angle of incidence. Plane wave reflection coefficients are obtained for the situation when the material mentioned above forms a transition layer between two homogeneous, elastic half-spaces. First and/or second-order discontinuities in material properties are permitted at the boundaries of the transition layer. Some numerical results are given.

Two techniques for the absorption of elastic waves using an artificial transition layer

Wave Motion ◽  
1997 ◽  
Vol 25 (1) ◽  
pp. 15-33 ◽  
Author(s):  
Yuan-Gao Zhang ◽  
Josef Ballmann
Keyword(s):  
Transition Layer ◽  
Elastic Waves

Promoting charge transfer in hyperbranched, trisoctahedral-shaped core–shell Au@PdPt nanoparticles by facet-dependent construction of transition layers as high performance electrocatalysts

2017 ◽  
Vol 5 (35) ◽  
pp. 18878-18887 ◽  
Author(s):  
Yahui Song ◽  
Cuixia Bi ◽  
Chenshuo Wu ◽  
Hongpeng He ◽  
Lihui Huang ◽  
...  
Keyword(s):  
Charge Transfer ◽  
Transition Layer ◽  
High Performance ◽  
Core Shell ◽  
Transition Layers ◽  
The Core ◽  
First Case

This is the first case of promoting charge transfer by facet-dependent construction of a transition layer between the core and the shell.

THE REFLECTION OF ELASTIC WAVES FROM TRANSITION LAYERS OF VARIABLE VELOCITY

Geophysics ◽  
1937 ◽  
Vol 2 (4) ◽  
pp. 357-363 ◽  
Author(s):  
Alfred Wolf
Keyword(s):  
Elastic Constants ◽  
Elastic Waves ◽  
Wave Length ◽  
Continuous Functions ◽  
Angle Of Incidence ◽  
Variable Velocity ◽  
Transition Layers ◽  
Coefficient Of Reflection ◽  
Continuous Waves ◽  
Explicit Formulae

Elastic waves are reflected not only from discontinuities in the medium in which they are propagated, but also from transition layers in which the elastic constants are continuous functions of position; the coefficient of reflection is then a function of wave length. Section 1 of this paper gives explicit formulae for the coefficient of reflection of continuous waves from such a layer, at vertical incidence. In Section 2 the manner of variation of the coefficient of reflection with the angle of incidence is discussed qualitatively. Finally, in Section 3, the shape of a pulse reflected from a transition layer is determined.

Three-Dimensional and Shell-Theory Analysis of Elastic Waves in a Hollow Sphere: Part 2—Numerical Results

1969 ◽  
Vol 36 (3) ◽  
pp. 440-444 ◽  
Author(s):  
A. H. Shah ◽  
C. V. Ramkrishnan ◽  
S. K. Datta
Keyword(s):  
Elastic Waves ◽  
Three Dimensional ◽  
Numerical Results ◽  
Mode Analysis ◽  
Theory Analysis ◽  
Frequency Spectra ◽  
The Past ◽  
Shell Analysis ◽  
Shell Equations ◽  
Thick Shells

In this Part 2 of the paper, numerical results obtained through an IBM 7044 digital computer are presented. Frequency values for the two classes of vibrations for different values of n are calculated from the exact frequency equations and also from the shell equations. Comparisons are made with the exact frequency spectra of those obtained from the present six-mode shell analysis and other available shell and membrane analyses. It is found that the lowest branches of the frequency spectra for the two classes of vibrations obtained by the six-mode analysis agree very well with the exact ones, even for very thick shells, whereas other shell analysis done in the past make erroneous predictions when the thickness-to-radius ratio of the shell is greater than 10 percent.

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