Nonlinear Dynamics of Cracked, Cantilevered Beam-like Structures Undergoing Large Deflections

The large vibrations of two cracked, fixed-free structures, respectively beam- and plate-like, are here reported and investigated. Both the consequences of damage and the nonlinear effects of geometrically-induced stiffening are considered and addressed. These latter terms are caused by the large deflections of the structure itself; they become non- negligible when the driving force's amplitude is (relatively) high. In turn, the damage was considered as a local source of bilinearity, arising from a breathing crack behaviour. The two case studies here proposed have been simulated by means of the finite element models of a steel beam with squared cross-section and of a thin, light-weight aluminium plate. Both the prismatic elements were considered as damaged with a single transverse edge crack, penetrating all along the structure's width. This simple preliminary study shows how, accordingly to the structure's material and cross-section, geometrical nonlinearities may or may not be safely neglected when characterising the damage-induced effects. A comparison of the wavelet levels of the response with and without geometrical nonlinearities and/or crack presence is also provided as an effective tool for damage detection in this context.