Eigenvalue imaging method for subsurface defects detection

Abstract

This paper proposes the eigenvalue imaging method to be independent of frequency and phase velocity and to characterize the Lamb-wave field. Lamb-waves play important roles in NDE fields. Being placed on the surface of a plate, a sound source excites several kinds of waves: (a) pressure and shear waves, (b) a Rayleigh wave, and (c) symmetric and anti-symmetric Lamb-waves traveling along the plate. The first two waves are utilized for traditional ultrasonic techniques such as pulse-echo methods. In contrast to these classical techniques, in which the wavelength is shorter than the plate thickness, the Lamb-wave has the advantage of propagating over large area. The variation of the Lamb-wave velocity, however, causes difficulties for interpretation of observed signals. It is important, therefore, to establish the crack detection criterion independent of local wave numbers. This paper proposes a novel imaging method which utilizes the 3rd and 4th eigenvalues of the covariance matrix, which is defined over the 4- dimensional vector space which is spanned by following components: (1) a vertical displacement, (2) its particle velocity, (3) the orthogonal pair of out-of-plane strains. This study shows that the 3rd eigenvalue detects a wave scattered by defects and the 4th one has an ability to localize defects.