Influences of Non-Locality on the Elastic Wave Surfaces in Elastic Media

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.

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

Geophysics ◽

10.1190/1.1442688 ◽

1989 ◽

Vol 54 (5) ◽

pp. 609-620 ◽

Cited By ~ 7

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.

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Complex elastic wave band structures in three-dimensional periodic elastic media

Journal of the Mechanics and Physics of Solids ◽

10.1016/s0022-5096(97)00023-9 ◽

1998 ◽

Vol 46 (1) ◽

pp. 115-138 ◽

Cited By ~ 37

Author(s):

Toshio Suzuki ◽

Paul K.L. Yu

Keyword(s):

Elastic Wave ◽

Three Dimensional ◽

Elastic Media ◽

Wave Band ◽

Band Structures

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Coupled Integral Equations for Microwave Induced Elastic Wave in Elastic Media

IEEE Transactions on Antennas and Propagation ◽

10.1109/tap.2010.2048869 ◽

2010 ◽

Vol 58 (7) ◽

pp. 2309-2317 ◽

Cited By ~ 3

Author(s):

Mei Song Tong ◽

Weng Cho Chew

Keyword(s):

Elastic Wave ◽

Integral Equations ◽

Elastic Media

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

Journal of Computational Acoustics ◽

10.1142/s0218396x01000796 ◽

2001 ◽

Vol 09 (02) ◽

pp. 703-718 ◽

Cited By ~ 79

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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