The Modelling of the Opening and Closure of a Crack

The paper presents a method which utilizes substructure normal modes to predict the vibration properties of a cantilever beam with a breathing transverse crack. The two segments of the cantilever beam, separated by the crack, are related to one another by time varying connection matrices representing the interaction forces. The connection matrices are expanded in a Fourier series leading to a classical eigenvalue problem. Subsequently, the initial formulation is extended to avoid interference of the crack interfaces with a time domain formulation. The Lagrange multipliers, used to enforce the exact continuity constraints when the crack is closed, produce the interfaces forces needed for the modelling of interface dry friction.