A New Theorem on Damage Localization and Its Implementation

摘要

A new theorem connecting changes in transfer matrices to the spatial location of stiffness related damage was recently introduced by the author.The theorem,designated as the dynamic damage locating vector theorem(DDLV)and its implementation as a damage localization algorithm are reviewed here.The theorem states that the span of the null space of the change in the transfer matrix(ΔG)contains vectors that are Laplace transforms of excitations for which the dynamic stress field is identically zero over the portion of the domain where the damage is located.A corollary states that if ΔG proves rank deficient at any s it is guaranteed to be rank deficient throughout the plane.A sufficient condition for rank deficiency is that the number of independent measurements is larger than the rank of the change in the stiffness matrix resulting from damage.Implementation of the theorem to localize damage using the stress field history is computationally taxing but an s-domain implementation leads to a practical algorithm.