×

Diffraction of elastic waves by a free wedge. Reduction to a singular integral equation. (Russian. English summary) Zbl 0706.73023

Some aspects concerning the diffraction of elastic waves by a free wedge are discussed. More specifically, the elastic homogeneous isotropic medium is bounded by a wedge defined in polar coordinates through \(\rho\geq 0\), \(| \theta | \leq \alpha\) (\(\alpha\) is a fixed angle). The boundary is assumed to be a free surface. The problem is to find the field (i.e. the longitudinal potential and the transversal one) subjected to: the Helmholtz equation, the asymptotic conditions at infinity, the boundary conditions. It is shown how the Sommerfeld integral associated with the Helmholtz equation and which gives the solution can be converted into a complex variable function problem known as Malyuzhinets problem (MP). The main idea of the paper is to convert the MP into a singular integral equation problem. For \(\alpha =0\) and \(\alpha =\pi /2\) one finds the usual integral representation. It is important to point that here only the idea of the method is sketched, the details are to be found elsewhere.
Reviewer: D.Stanomir

MSC:

74J20 Wave scattering in solid mechanics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35C15 Integral representations of solutions to PDEs
PDFBibTeX XMLCite
Full Text: EuDML