An input-output damage detection method using static equivalent formulation of dynamic vibration

In this study, a new damage detection method is developed which directly uses input-output data of a forced vibration of a structure. For this, the dynamic vibration formulation of an FE model has been integrated within the time domain of the vibration of the structure. Also, the static condensation scheme is used to reduce required measured degrees of freedom (DOF's). Hence, the main characteristic of the proposed method is that it just uses translational time history response of a structure at specified nodes corresponding to the finite element model of that structure. Also, the only required data from the original FE model of the structure is its stiffness matrix. To assess the capability of the proposed method in damage detection in beam type structures a cantilever beam is studied. Not only can the method locate damaged elements, but also the quantity of damage in every damaged element is computed successfully. Also, it has been shown that as the frequency of the applied load in simulated experiment approaches to the first natural frequency of the beam, the accuracy dwindles significantly. Hence, for obtaining more reliable results, the frequency of the applied load shall be far enough from the first natural frequency of the free vibration of the beam. The results demonstrate that the integrated displacements in specified nodes through the time of vibration carry enough information about damages in elements and the proposed method can be successfully used for damage detection in beam type structures.