Identification of the nonlinear behavior of a cracked RC beam through the statistical analysis of the dynamic response

This study investigates a new identification procedure suitable to deal with nonlinear systems. The proposed approach is made up of three main parts: system excitation with a band-limited white noise, solution of the Fokker–Planck equation that describes the motion of the structure in a parametric form and identification of the unknown system parameters by minimizing a suitable functional. The new procedure is able, for instance, to assess the severity of cracking caused by the shrinkage or by the overcoming of the concrete tensile strength in reinforced concrete (RC) structures. Cracked RC elements, in fact, exhibit a nonlinear behaviour due to different values of the flexural stiffness that depends on the opening of the cracks. Some numerical simulations allowed verifying the applicability of the procedure.