Damage Detection in Truss Structures Using Modal Expansion and Flexibility Matrix

. In this study, a new index for damage detection in truss structures is presented. The technique exploits incomplete mode shapes obtained from pseu do-experimental data which mimic the records of a limited number of sensors placed on the structure. The modes are completed using a multi-step modal ex pansion technique based on the subspace iteration method. Stiffness and mass matrices are computed only after the dynamic condensation matrix converges, thus making the iteration procedure computationally efficient. Once the modes are expanded and mass normalized, the identification method is developed by computing the flexibility matrices of healthy and damaged structures. Each flexibility matrix is approximated as the product of the first circular frequencies and complete mode shapes of the truss where each column represents the node displacements associated with unitary forces applied to the corresponding de gree of freedom. From the flexibility matrix, it is possible to construct a matrix of strain changes induced by the presence of damage in the structure. The dam age identification exploits a novel index based on Singular Value Decomposi tion of the strain change matrix and identifies the damaged elements as bars with the highest values. Two numerical examples on planar truss structures show the potentialities of the method.