An Angle-between-String-and-Horizon flexibility for structural damage detection

A new flexibility called Angle-between-String-and-Horizon Flexibility, ASHF for short is defined and derived. The proposed flexibility is synthesized from measured modal frequencies and Angle-between-String-and-Horizon (ASH) mode shapes which are expressed in terms of translational mode shapes. Physically, the elements in ith column of ASHF represent the ASHs of each element resulting from a unit moment in the form of a pair of parallel forces with equal amplitudes but opposite directions applied at two nodes of the ith element. The diagonal entries or the maximum absolute values of elements in each column of the difference between ASHFs for the pre- and post-damaged structures are designated as damage indicators. Multiple damage locations are directly indicated by step distribution of the damage indicators for structures with arbitrary support conditions. Moreover, magnitudes of steps are in relevancy to damage extent and can indicate the damage severity. The applicability of the proposed method for damage detection is studied by numerically investigating the influence of number of modes and measurement points with a cantilever beam.