On the identification of a crack in 3D acoustics

摘要

This paper addresses the problem of the identification of a planar crack in 3D acoustics. The measurements are arbitrary transient inputs applied to the boundary of the solid and the corresponding response. We show that the overdetermined boundary data allows the explicit reconstruction of the crack plane and the crack geometry. The approach is based on the construction of a reciprocity gap the definition of a series of well chosen adjoint states. This approach conducts conducts to direct identifications of the host plane of the crack and to a closed-form formula for the geometry of the crack. Compared to classical solution of similar inverse problems in acoustics this method applies to bounded bodies and does not use the Born approximation in the frequency domain.