Assessment of damage in continuum structures based on incomplete modal information

An identification technique based on the characteristic equations for structural dynamic systems is developed to assess damage in continuum structures, where the information about incomplete modal data can be directly utilised. The structural damage model is assumed to be associated with a reduction of a contribution to the element stiffness matrix emanating from a given Gauss point, equivalent to a scalar reduction of the material modulus, which characterises material at the Gauss point level. The incomplete mode shapes for the damaged structure can be expanded into complete mode shapes by using the actual measured modal readings and assuming the unknown modal data for the remaining dimension. A computational technique based on the Gauss–Newton Least Squares technique is developed for the inverse prediction of structural damage, where both the location and the extent of structural damage can be correctly determined using only a limited amount of measurements of incomplete modal data. Finally, numerical examples for continuum structures, restricted here to a plane stress model problem and plate bending model problem, are utilised to demonstrate the effectiveness of the proposed approach.