Study of generalized eigenfunctions of a perturbed isotropic elastic half-space

✍ Scribed by Yves Dermenjian; Patricia Gaitan

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 214 KB
• Volume: 23
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(20000525)23:8<685::aid-mma109>3.0.co;2-i

✦ Synopsis

We consider the self-adjoint operator governing the propagation of elastic waves in a perturbed isotropic half-space (perturbation with compact support of a homogeneous isotropic half-space) with a free boundary condition. We propose a method to obtain, numerical values included, a complete set of generalized eigenfunctions that diagonalize this operator. The "rst step gives an explicit representation of these functions using a perturbative method. The unbounded boundary is a new di$culty compared with the method used by Wilcox [25], who set the problem in the complement of bounded open set. The second step is based on a boundary integral equations method which allows us to compute these functions. For this, we need to determine explicitly the Green's function of (A ! ), where A is the selfadjoint operator describing elastic waves in a homogeneous isotropic half-space.