Abstract
Reflection and transmission of a longitudinal wave by a periodic array of inclined two-dimensional cracks has been investigated. By using the Betti-Rayleigh reciprocity relation, a pair of singular integral equations has been derived for the crack-opening displacements. The singular integral equations have been solved by the use of the boundary element method. Reflection and transmission coefficients of zeroth order have been expressed in terms of the crack-opening displacements by an application of the Betti-Rayleigh reciprocity relation. These coefficients have been computed for normal and oblique incidence, for collinear and inclined cracks, and for various values of the wave number. The results for normal incidence on collinear cracks have been compared with earlier results, and excellent agreement has been obtained. The results for oblique wave incidence or inclined cracks show mode conversion, and they display the dependence of the reflection and the transmission coefficients on the frequency of the incident wave.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 59-72 |
| Number of pages | 14 |
| Journal | Wave Motion |
| Volume | 10 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1988 |
Funding
This work was carried out under Contract DE FG02-86-ER 13484w ith the Departmento f Office of Basic Energy Sciences,E ngineeringR esearchP rogram.
ASJC Scopus subject areas
- Modeling and Simulation
- General Physics and Astronomy
- Computational Mathematics
- Applied Mathematics