Generation of higher harmonics in longitudinal vibration of beams with breathing cracks

Classical nonlinear vibration methods used for structural damage detection are often based on higher- and sub-harmonic generation. However, nonlinearities arising from sources other than damage – e.g. boundary conditions or a measurement chain – are a primary concern in these methods. This paper focuses on localisation of damage-related nonlinearities based on higher harmonic generation. Numerical and experimental investigations in longitudinal vibration of beams with breathing cracks are presented. Numerical modelling is performed using a two-dimensional finite element approach. Different crack depths, locations and boundary conditions are investigated. The results demonstrate that nonlinearities in cracked beams are particularly strong in the vicinity of damage, allowing not only for damage localisation but also for separation of crack induced nonlinearity from other sources of nonlinearities.