Huygens’ principle, radiation conditions, and integral formulas for the scattering of elastic waves

1976 ◽  
Vol 59 (6) ◽  
pp. 1361-1371 ◽  
Author(s):  
Yih‐Hsing Pao ◽  
Vasundara Varatharajulu
Keyword(s):  
Elastic Waves ◽  
Integral Formulas ◽  
Scattering Of Elastic Waves ◽  
Huygens Principle ◽  
Radiation Conditions

Numerical Formulation to Study Fluid-Solid Interfaces Excited by Elastic Waves

2010 ◽  
Vol 449 ◽  
pp. 54-61 ◽  
Author(s):  
Alejandro Rodríguez-Castellanos ◽  
Esteban Flores Mendez ◽  
Francisco José Sánchez-Sesma ◽  
José Efraín Rodríguez-Sánchez
Keyword(s):  
Elastic Waves ◽  
Single Layer ◽  
Physical Reality ◽  
Boundary Integral ◽  
Intermediate Step ◽  
Diffracted Waves ◽  
Scattering Of Elastic Waves ◽  
Numerical Formulation ◽  
Physical Insight ◽  
Huygens Principle

In this paper, the scattering of elastic waves in a fluid-solid interface is researched. The Indirect Boundary Element Method (IBEM) was used to study this wave propagation phenomenon in a 2D fluid-solid model. The source, represented by a Hankel´s function of the second kind, is always applied in the fluid. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. The approach presented is usually called IBEM as the sources’ strengths should be obtained as an intermediate step. This indirect formulation can give a deep physical insight to the analyst on the generated diffracted waves, because it is closer to the physical reality and can be regarded as a realization of Huygens’ Principle, which mathematically is fully equivalent to the classical Somigliana’s representation theorem. In order to gauge accuracy, the method was tested by comparing it to an analytical solution. A near interface pulse generates scattered waves that can be registered by sensors located in the fluid. Results are presented in time domain, where several aspects related to the different wave types that emerge from this kind of problems are pointed out.

Scattering of elastic waves by a circular hole in the unsaturated soil

2020 ◽  
Vol 137 ◽  
pp. 106295
Author(s):  
Jian-Fei Lu ◽  
Meng-Qin Shi ◽  
Qing-Song Feng
Keyword(s):  
Circular Hole ◽  
Unsaturated Soil ◽  
Elastic Waves ◽  
Scattering Of Elastic Waves

Multiple scattering of elastic waves by a distribution of identical spheres

1990 ◽  
Vol 31 (11) ◽  
pp. 2619-2625 ◽  
Author(s):  
D. D. Phanord ◽  
N. E. Berger
Keyword(s):  
Multiple Scattering ◽  
Elastic Waves ◽  
Scattering Of Elastic Waves

Fast and slow interaction of elastic waves with platonic clusters

2011 ◽  
Vol 467 (2136) ◽  
pp. 3509-3529 ◽  
Author(s):  
Michael H. Meylan ◽  
Ross C. McPhedran
Keyword(s):  
Elastic Waves ◽  
Early Time ◽  
Approximate Solutions ◽  
Wave Profile ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Analytical Extension ◽  
Scattering Of Elastic Waves ◽  
Classical Models ◽  
The Time Domain

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

Scattering of elastic waves by localized anisotropic inclusions

1990 ◽  
Vol 87 (6) ◽  
pp. 2300-2309 ◽  
Author(s):  
Ari Ben‐Menahem ◽  
Richard L. Gibson
Keyword(s):  
Elastic Waves ◽  
Scattering Of Elastic Waves
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