Chaotic Dynamics of Cantilever Beams with Breathing Cracks

A nonlinear dynamic system with a finite number of degrees of freedom, which describes the forced oscillations of a beam with two breathing cracks, is obtained. The cracks are located on opposite sides of the beam. The Bubnov-Galerkin method is used to derive the nonlinear dynamic system. Infinite sequences of period-doubling bifurcations cause chaotic oscillations and are observed at the second-order subharmonic resonance. Poincaré sections and spectral densities are calculated to analyze the properties of chaotic oscillations. In addition, Lyapunov exponents are calculated to confirm the chaotic behavior. As follows from the numerical analysis, chaotic oscillations arise as a result of the nonlinear interaction between cracks.