Vibration analysis of a cracked beam with a breathing crack by using a novel cracked beam element

Abstract To investigate the vibrational response of a beam structure with a breathing crack, a new cracked beam element model is proposed, in which the curvature is incorporated as a fundamental unknown quantity at the nodes. A dynamic model of the beam with a breathing crack is developed using the finite element method to analyze the influence of crack size on both displacement and strain mode shapes. The influence of excitation frequency, excitation force amplitude, and crack parameters on vibration response of a beam with a breathing crack is investigated. The results demonstrate that strain mode shapes exhibit higher sensitivity to crack damage compared to displacement mode shapes. When the cracked beam structure is excited at frequencies fΩ=1/3f₁ or fΩ=1/2f₁, its frequency spectrum response contains several harmonic components. Among these, a harmonic component at the first natural frequency f₁ is always present and typically exhibits the largest amplitude. Additionally, several sidebands exist around this component at frequencies that satisfy the relation nfΩ± f₁ (n = 1, 2, …,). The spacing between these sidebands is equal to the excitation frequency fΩ. This spectral characteristic can serve as a qualitative indicator for determining crack defects in the beam structures.