Using the exact element method and modal frequency changes to identify distributed damage in beams

An identification procedure is presented for the stiffness distribution of beam elements, under an approach based on changes in a few natural frequencies. The stiffness distribution along the beam is represented by a polynomial function, while its coefficients are the unknown in the identification procedure. Thus, the procedure suits a continuous damage scenario, which in the case of reinforced concrete elements represents an advanced distributed cracked zone.In order to reduce the number of degrees of freedom of the analytical model, the algorithm employs the “exact” element method. The identification procedure constructs a sensitivity matrix using a reference stage of a healthy beam. This matrix is constructed once for each healthy beam. The stiffness distribution function is then obtained using a given set of frequencies in a damage condition. The only modal parameters required are, therefore, a subset of pre- and post-damage vibration frequencies.The presented procedure is validated on single and continuous beams using analytical and varied modal frequencies. In order to demonstrate its practicability, the procedure is validated using experimental data available from the literature.