Diffraction of time-harmonic elastic waves by a cylindrical obstacle

1976 ◽  
Vol 32 (2) ◽  
pp. 97-144 ◽  
Author(s):  
T. H. Tan
Keyword(s):  
Elastic Waves ◽  
Cylindrical Obstacle ◽  
Time Harmonic

Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity

2012 ◽  
Vol 131 (4) ◽  
pp. 2570-2578 ◽  
Author(s):  
Guangxin Tang ◽  
Laurence J. Jacobs ◽  
Jianmin Qu
Keyword(s):  
Elastic Waves ◽  
Elastic Inclusion ◽  
Quadratic Nonlinearity ◽  
Time Harmonic

scholarly journals Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves

2017 ◽  
Vol 33 (3) ◽  
pp. 035013 ◽  
Author(s):  
Elena Beretta ◽  
Maarten V de Hoop ◽  
Elisa Francini ◽  
Sergio Vessella ◽  
Jian Zhai
Keyword(s):  
Boundary Value Problem ◽  
Elastic Waves ◽  
Boundary Value ◽  
Lipschitz Stability ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem ◽  
Time Harmonic

scholarly journals Approximate local Dirichlet-to-Neumann map for three-dimensional time-harmonic elastic waves

2015 ◽  
Vol 297 ◽  
pp. 62-83 ◽  
Author(s):  
Stéphanie Chaillat ◽  
Marion Darbas ◽  
Frédérique Le Louër
Keyword(s):  
Elastic Waves ◽  
Three Dimensional ◽  
Time Harmonic ◽  
Dirichlet To Neumann Map

3D modeling of time-harmonic elastic waves in anisotropic media using a direct Helmholtz solver

2012 ◽  
Author(s):  
Shen Wang ◽  
Maarten V. de Hoop ◽  
Jianlin Xia ◽  
Xiaoye Li
Keyword(s):  
3D Modeling ◽  
Elastic Waves ◽  
Anisotropic Media ◽  
Time Harmonic

Elastic Waves in Inhomogeneous Elastic Media

1972 ◽  
Vol 39 (3) ◽  
pp. 696-702 ◽  
Author(s):  
Adnan H. Nayfeh ◽  
Siavouche Nemat-Nasser
Keyword(s):  
Perturbation Method ◽  
Incident Wave ◽  
Elastic Waves ◽  
Harmonic Waves ◽  
Elastic Media ◽  
Time Harmonic ◽  
Special Cases ◽  
Inhomogeneous Elastic Media ◽  
Inhomogeneous Elastic Medium ◽  
Large Frequency

The WKB solution is derived together with the condition for its validity for elastic waves propagating into an inhomogeneous elastic medium. Large frequency expansion solution is also derived. It is found that the WKB solution agrees with that derived for large frequencies when the frequency approaches infinity. Some exact solutions are deduced from the WKB solution. Finally, we consider motions in medium which consists of a material with harmonic periodicity. The solution is obtained by means of a perturbation method. It is shown that, only when the wavelength of the incident wave is small compared with the periodicity-length of the material, the WKB solution constitutes a good approximation. When the wavelength is comparable with this periodicity-length, then, in certain special cases, the material cannot maintain time-harmonic waves; such harmonic waves are not “stable.” These and other solutions are discussed in detail.

Diffraction of elastic waves by a penny-shaped crack

1981 ◽  
Vol 378 (1773) ◽  
pp. 263-285 ◽  
Keyword(s):  
Integral Equation ◽  
Boundary Value Problem ◽  
Unique Solution ◽  
Double Layer ◽  
Elastic Waves ◽  
Boundary Value ◽  
Elastic Solid ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Crack

Consider an infinite elastic solid containing a penny-shaped crack. We suppose that time-harmonic elastic waves are incident on the crack and are required to determine the scattered displacement field u i . In this paper, we describe a new method for solving the corresponding linear boundary-value problem for u i , which we denote by S. We begin by defining an ‘elastic double layer’; we prove that any solution of S can be represented by an elastic double layer whose ‘density’ satisfies certain conditions. We then introduce various Green functions and define a new crack Green function, G ij , that is discontinuous across the crack. Next, we use G ij to derive a Fredholm integral equation of the second kind for the discontinuity in u i across the crack. We prove that this equation always has a unique solution. Hence, we are able to prove that the original boundary-value problem S always possesses a unique solution, and that this solution has an integral representation as an elastic double layer whose density solves an integral equation of the second kind.

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