Non-linear dynamic response to simple harmonic excitation of a thin-walled beam with a breathing crack

The dynamic response of a thin-walled beam with a breathing crack is studied by employing a refined one-dimensional model introduced for such purpose. It is shown that, due to the non-linearity of breathing, some effects take place which are impossible by using a completely open crack model. Even with the simplest of sinusoidal excitations, the system under study reveals a rich and complex dynamics. Some of the topics emphasized in the article are self-excitation of harmonic resonances, period doubling and the presence of quasi-periodic motion. Furthermore, the possibility of chaotic vibrations is analyzed.