Identification of a non-linear spring through the Fokker–Planck equation

Standard methods for the dynamic identification of civil engineering structures and mechanical systems generally rely on the determination of eigenfrequencies/eigenvectors and damping. A basic assumption for the use of these methods is the linear elastic behaviour of the tested structures. Nevertheless many structures exhibit a non-linear behaviour even at low levels of external excitation. For instance, reinforced concrete structures cracked by shrinkage or by the overcoming of the concrete tensile strength, exhibit different values of the flexural stiffness depending on the opening of the cracks. In the present paper a new methodology is presented to identify the characteristics of a non-linear mechanical system using the Fokker–Plank Equation (FPE) that allows evaluating the probability density function of the response of structural systems loaded with Gaussian white noise.