scholarly journals Low frequency scattering of elastic waves by a cavity using a matched asymptotic expansion method

1995 ◽  
Vol 37 (1) ◽  
pp. 99-120 ◽  
Author(s):  
L. Bencheikh
Keyword(s):  
Elastic Waves ◽  
Elliptic Boundary ◽  
Low Frequency ◽  
Expansion Method ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
P Wave ◽  
Matched Asymptotic Expansion ◽  
Scattering Of Elastic Waves ◽  
Diffraction Of Elastic Waves

AbstractThis work deals with low-frequency asymptotic solutions using the method of matched asymptotic expansions. It is based on two papers by Buchwald [3] and Buchwald and Tran Cong [4] who studied the diffraction of elastic waves by a small circular cavity and a small elliptic cavity, respectively, in an otherwise unbounded domain. Here we clarify and systematize some aspects of their work and extend it to the diffraction of elastic waves by a small cylindrical cavity with a hypotrochoidal boundary. Results for the case of an incident P-wave are compared, in the special case of an elliptic boundary, with the results from the numerical solution of the boundary integral equation method.

Diffraction of elastic waves from object in layer with slightly corrugated surface

2017 ◽  
Vol 23 (9) ◽  
pp. 1249-1262 ◽  
Author(s):  
Khaled M Elmorabie ◽  
Rania R Yahya
Keyword(s):  
Elastic Waves ◽  
Perturbation Technique ◽  
Scattering Problem ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Harmonic Load ◽  
Frequency Range ◽  
Corrugated Surfaces ◽  
Geometrical Shapes ◽  
Diffraction Of Elastic Waves

This work is concerned with the influence of corrugated surfaces on waves diffracted from an object in an elastic layer. A boundary value problem is formulated to simulate an anti-plane problem for a harmonic load acting on the upper surface of the layer. By using the boundary integral equation method and the perturbation technique, the considered problem is reduced to a pair of integral equations. By constructing the Green’s function, the scattering problem in a one-mode frequency range is solved. To check the validity of the proposed technique, several numerical examples for different geometrical shapes of the corrugated bottom are presented.

Hydrodynamic Interactions of the Truncated Porous Vertical Circular Cylinder With Water Waves

2018 ◽  
Author(s):  
Charaf Ouled Housseine ◽  
Sime Malenica ◽  
Guillaume De Hauteclocque ◽  
Xiao-Bo Chen
Keyword(s):  
Circular Cylinder ◽  
Porous Body ◽  
Wave Diffraction ◽  
Water Waves ◽  
Expansion Method ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Diffraction Radiation ◽  
Linear Potential ◽  
Eigenfunction Expansion Method

Wave diffraction-radiation by a porous body is investigated here. Linear potential flow theory is used and the associated Boundary Value Problem (BVP) is formulated in frequency domain within a linear porosity condition. First, a semi-analytical solution for a truncated porous circular cylinder is developed using the dedicated eigenfunction expansion method. Then the general case of wave diffraction-radiation by a porous body with an arbitrary shape is discussed and solved through Boundary Integral Equation Method (BIEM). The main goal of these developments is to adapt the existing diffraction-radiation code (HYDROSTAR) for that type of applications. Thus the present study of the porous cylinder consists a validation work of (BIEM) numerical implementation. Excellent agreement between analytical and numerical results is observed. Porosity influence on wave exciting forces, added mass and damping is also investigated.

Diffraction of Elastic Waves by a Cylindrical Nanohole

2014 ◽  
Vol 526 ◽  
pp. 145-149 ◽  
Author(s):  
Li Wang ◽  
Pei Jun Wei ◽  
Xi Qiang Liu ◽  
Gui Zhang
Keyword(s):  
Plane Wave ◽  
Cross Section ◽  
Elastic Waves ◽  
Surface Stress ◽  
Scattering Amplitude ◽  
Expansion Method ◽  
Plane Wave Expansion ◽  
Plane Wave Expansion Method ◽  
Stress Effects ◽  
Diffraction Of Elastic Waves

Diffraction of in-plane wave and out-plane wave by a cylindrical nanohole is investigated. The surface elastic theory is used to consider the surface stress effects and to derive the boundary condition on the surface of the nanohole. The plane wave expansion method is applied to obtain the scattering waves. The scattering cross section and far-field scattering amplitude are numerically evaluated. The influences of surface stress are discussed based on the numerical results.

scholarly journals Diffraction of Elastic Waves in Fluid-Layered Solid Interfaces by an Integral Formulation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
J. E. Basaldúa-Sánchez ◽  
D. Samayoa-Ochoa ◽  
J. E. Rodríguez-Sánchez ◽  
A. Rodríguez-Castellanos ◽  
M. Carbajal-Romero
Keyword(s):  
Elastic Waves ◽  
Single Layer ◽  
Elastic Solid ◽  
Boundary Integral ◽  
Wave Number ◽  
Intermediate Step ◽  
Solid Models ◽  
Time Domains ◽  
Scattering Of Elastic Waves ◽  
Layered Solid

In the present communication, scattering of elastic waves in fluid-layered solid interfaces is studied. The indirect boundary element method is used to deal with this wave propagation phenomenon in 2D fluid-layered solid models. The source is represented by Hankel’s function of second kind and this is always applied in the fluid. Our method is an approximate boundary integral technique which is based upon an integral representation for scattered elastic waves using single-layer boundary sources. This approach is typically called indirect because the sources’ strengths are calculated as an intermediate step. In addition, this formulation is regarded as a realization of Huygens’ principle. The results are presented in frequency and time domains. Various aspects related to the different wave types that emerge from this kind of problems are emphasized. A near interface pulse generates changes in the pressure field and can be registered by receivers located in the fluid. In order to show the accuracy of our method, we validated the results with those obtained by the discrete wave number applied to a fluid-solid interface joining two half-spaces, one fluid and the other an elastic solid.

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