Journal of Applied Mathematics
Volume 2012 (2012), Article ID 525431, 10 pages
Research Article

Spectral Ratios for Crack Detection Using P and Rayleigh Waves

1Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, Gustavo A. Madero, 07730 México, DF, Mexico
2Centro de Investigación en Matemáticas, Jalisco s/n, Mineral de Valenciana, 36240 Guanajuato, GTO, Mexico
3Instituto Politécnico Nacional, Escuela Superior de Ingeniería y Arquitectura, UP Zacatenco, 07738 México, DF, Mexico
4Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica, UP Azcapotzalco, 02250 México, DF, Mexico

Received 2 April 2012; Accepted 7 June 2012

Academic Editor: Kai Diethelm

Copyright © 2012 Enrique Olivera-Villaseñor et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain numerical results to help the detection and characterization of subsurface cracks in solids by the application of P and Rayleigh elastic waves. The response is obtained from boundary integral equations, which belongs to the field of elastodynamics. Once the implementation of the boundary conditions has been done, a system of Fredholm integral equations of the second kind and order zero is found. This system is solved using the method of Gaussian elimination. Resonance peaks in the frequency domain allow us to infer the presence of cracks using spectral ratios. Several models of cracked media were analyzed, where effects due to different crack orientations and locations were observed. The results obtained are in good agreement with those published in the references.