Analysis on nonlinear vibration of breathing cracked beam

Abstract The nonlinear behaviors of breathing cracked beam vibration are investigated. A continuous model based on Timoshenko beam theory is established, whose breathing effect is described by signal function in mathematics to simulate bilinear stiffness. A semi-analytical approach to solve the problem is developed by spatial difference discretization and transfer matrix method, in which local linearization and the Pade approximation are employed. The numerical results of validated examples have good agreement with experiments and FEM. As a typical indicator to breathing crack, the super-resonance responses under harmonic and fast frequency-sweep excitation are analyzed, such as waveforms, phase portraits and FFT results.