Damage identification in beams based on the observation of frequencies and modal curvatures

This work investigates numerically and experimentally the dynamic response of a free-free beam in its undamaged and damaged states, in terms of natural frequencies and modal curvatures. The damage consists of a height reduction extending to all the base of the cross section, and is described by three parameters, that are: depth of the height reduction, extension, location of its axis of symmetry along the beam axis. The resulting direct problem is solved via a 2D plane-stress finite element analysis, covering a dense grid of the three damage parameters. Several experimental tests are conducted on steel beams, covering selected values of damage parameters, and using strain gauges with grids of different lengths to understand how this sensor characteristic affects the measurement of the strain. The natural frequencies and modal curvatures obtained from the solution of this direct eigenvalue problem are compared to their experimental counterpart to evaluate the capability of the model to describe real data. Furthermore, the solution of the inverse problem of damage identification is carried out, providing some insight into the identifiability of the three damage parameters. The solution of the inverse problem is approached minimizing objective functions that measure the differences between numerical and pseudo-experimental and experimental variations of natural frequencies and/or of modal curvatures in the undamaged and damaged states.