Forced Nonlinear Bending Vibrations of Beams with Two Breathing Cracks

The nonlinear bending vibrations of the cracked beams are studied. The beam structure has two breathing cracks, which are described by two contact parameters. The nonlinear beam vibrations are described by finite degrees of freedom nonlinear dynamical system, which are derived by using the Galerkin technique. The numeric continuation method is implemented to study the nonlinear forced vibrations of beams. The bifurcation behavior of forced vibrations is analyzed numerically. The period- doubling bifurcations and the Naimark-Sacker bifurcations of the cracked beam are analyzed.