Localization and Quantification of Breathing Crack

The possibility of localizing and quantifying a crack in a vibrating structure based on measured vibration amplitudes of the first and second harmonic in some locations of the structure and utilizing the mathematical model of an undamaged system, will be the focus of this paper. The structure is modeled by means of the finite element method. The effect of the breathing crack is modeled by the nonlinear (bilinear) stiffness of the element with the crack. The excitation of the system is characterized by the simultaneous effect of static and dynamic harmonic load. The Fourier series representations of the approximate analytical solution of a weakly bilinear system was used to obtain the localization and quanification a weak bilinearity. The method was documented on an elementary example, in which simulated measured data were determined by the use of the numerical solution of the nonlinear analytical model of a structure with a crack.