Geometrically non-linear steady state periodic forced response of a clamped–clamped beam with an edge open crack

The present work is concerned with the study of the geometrically non-linear steady state periodic forced response of a clamped–clamped beam containing an open crack. The model based on Hamiltonʼs principle and spectral analysis, previously used to investigate various non-linear vibration problems, is used here to determine the effect of the excitation frequency and level of the applied harmonic force, concentrated at the cracked beam middle span, on its dynamic response at large vibration amplitudes. The formulation uses the “cracked beam functions”, denoted as ‘CBF’, previously defined in recent works, obtained by combining the linear theory of vibration and the linear fracture mechanics theory. The crack has been modelled as a linear spring which, for a given depth, the spring constant remains the same for both directions. The results obtained may be used to detect cracks in vibrating structures, via examination of the qualitative and quantitative changes noticed in the non-linear dynamic behaviour, which is commented in the conclusion.