Coupled Integral Equations for Microwave Induced Elastic Wave in Elastic Media

2010 ◽  
Vol 58 (7) ◽  
pp. 2309-2317 ◽  
Author(s):  
Mei Song Tong ◽  
Weng Cho Chew
Keyword(s):  
Elastic Wave ◽  
Integral Equations ◽  
Elastic Media

scholarly journals EXTENSION OF THE PUFEM TO ELASTIC WAVE PROPAGATION IN LAYERED MEDIA

2012 ◽  
Vol 20 (02) ◽  
pp. 1240006 ◽  
Author(s):  
O. LAGHROUCHE ◽  
A. EL-KACIMI ◽  
J. TREVELYAN
Keyword(s):  
Finite Element Method ◽  
Elastic Wave ◽  
Rayleigh Waves ◽  
Partition Of Unity ◽  
Elastic Media ◽  
Elastic Wave Equation ◽  
Wave Problems ◽  
Numer Math ◽  
Basis Decomposition ◽  
Transmission And Reflection

This work deals with the extension of the partition of unity finite element method (PUFEM) "(Comput. Meth. Appl. Mech. Eng.139 (1996) pp. 289–314; Int. J. Numer. Math. Eng.40 (1997) 727–758)" to solve wave problems involving propagation, transmission and reflection in layered elastic media. The proposed method consists of applying the plane wave basis decomposition to the elastic wave equation in each layer of the elastic medium and then enforce necessary continuity conditions at the interfaces through the use of Lagrange multipliers. The accuracy and effectiveness of the proposed technique is determined by comparing results for selected problems with known analytical solutions. Complementary results dealing with the modeling of pure Rayleigh waves are also presented where the PUFEM model incorporates information about the pressure and shear waves rather than the Rayleigh wave itself.

Exact Green’s functions using leaking modes for axisymmetric boreholes in solid elastic media

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 609-620 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
Wave Propagation ◽  
Fourier Transform ◽  
Elastic Wave ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Media ◽  
Complex Frequency ◽  
Residue Theory

By choosing appropriate paths of integration in both the complex frequency ω and complex wavenumber k planes, exact Green’s functions for elastic wave propagation in axisymmetric fluid‐filled boreholes in solid elastic media are expressed completely as sums of modes. There are no contributions from branch line integrals. The integrations with respect to k are performed exactly using Cauchy residue theory. The remaining integrations with respect to ω are then carried out partly by using the fast Fourier transform (FFT) and partly by using another numerical method. Provided that the number of points in the FFT can be taken sufficiently large, there are no restrictions on distance. The method is fast, accurate, and easy to apply.

Elastic Wave Scattering From an Interface Crack in a Layered Half Space Submerged in Water: Part I: Applied Tractions at the Liquid-Solid Interface

1986 ◽  
Vol 53 (2) ◽  
pp. 326-332 ◽  
Author(s):  
S. M. Gracewski ◽  
D. B. Bogy
Keyword(s):  
Elastic Wave ◽  
Integral Equations ◽  
Half Space ◽  
Interface Crack ◽  
Wave Scattering ◽  
Plane Waves ◽  
Crack Tip ◽  
Solid Interface ◽  
Elastic Wave Scattering ◽  
Layered Half Space

In Part I of this two-part paper, the analytical solution of time harmonic elastic wave scattering by an interface crack in a layered half space submerged in water is presented. The solution of the problem leads to a set of coupled singular integral equations for the jump in displacements across the crack. The kernels of these integrals are represented in terms of the Green’s functions for the structure without a crack. Analysis of the integral equations yields the form of the singularities of the unknown functions at the crack tip. These singularities are taken into account to arrive at an algebraic approximation for the integral equations that can then be solved numerically. Numerical results in the form of crack tip stress intensity factors are presented for the cases in which the incident disturbance is a harmonic uniform normal or shearing traction applied at the liquid-solid interface. These results are compared with a previously published solution for this problem in the absence of the liquid. In Part II, which immediately follows Part I in the same journal issue, the more realistic disturbances of plane waves and bounded beams incident from the liquid are considered.

WAVE PROPAGATION IN 2-D ELASTIC MEDIA USING A SPECTRAL ELEMENT METHOD WITH TRIANGLES AND QUADRANGLES

2001 ◽  
Vol 09 (02) ◽  
pp. 703-718 ◽  
Author(s):  
DIMITRI KOMATITSCH ◽  
ROLAND MARTIN ◽  
JEROEN TROMP ◽  
MARK A. TAYLOR ◽  
BETH A. WINGATE
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Spectral Element Method ◽  
Mass Matrix ◽  
Spectral Element ◽  
Elastic Wave Propagation ◽  
Elastic Media ◽  
Spectral Element Methods ◽  
Fekete Points ◽  
Element Method

We apply a spectral element method based upon a conforming mesh of quadrangles and triangles to the problem of 2-D elastic wave propagation. The method retains the advantages of classical spectral element methods based upon quadrangles only. It makes use of the classical Gauss–Lobatto–Legendre formulation on the quadrangles, while discretization on the triangles is based upon interpolation at the Fekete points. We obtain a global diagonal mass matrix which allows us to keep the explicit structure of classical spectral element solvers. We demonstrate the accuracy and efficiency of the method by comparing results obtained for pure quadrangle meshes with those obtained using mixed quadrangle-triangle and triangle-only meshes.

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