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Shock and Vibration
Volume 2015, Article ID 195682, 9 pages
http://dx.doi.org/10.1155/2015/195682
Research Article

Inverse Shape Reconstruction of Inner Cavities Using Guided SH-Waves in a Plate

1State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, 29 Yudao Jie, Nanjing 210016, China
2Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan

Received 24 December 2014; Accepted 16 February 2015

Academic Editor: Tony Murmu

Copyright © 2015 Bin Wang 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.

Abstract

The paper proposes an inverse reconstruction method for inner cavities in a 2D plate using guided SH-waves. When a pure incident wave mode is sent toward the flaw area, reflected waves are observed at the far field due to mode conversion. From wave scattering theory, the reflected wave field is expressed by an integral over the unknown flaw surface concerning the total wave field. By the introduction of Born approximation and far-field expressions of Green’s function, it is found that the reflection coefficient for the mode of the same order as that of the incident mode is related to the unknown shape of the cavity by Fourier transform relations. By mathematical deduction, we show that if the basic (0th-order) symmetric and the 1st-order antisymmetric modes are used as incident waves, the locations and shapes of upper and lower boundaries of the cavity can be reconstructed. Numerical examples are illustrated in the paper, and a proper condition for applying this method is discussed. The research can act as a basis of nondestructive inspection for latent flaws within more complicated structures.