Geometrically non-linear forced vibrations of a clamped-clamped beam with an edge crack: a single mode approach

摘要

The present work is concerned with the study of the geometrically non-linear dynamic steady state periodic forced response of a clamped-clamped beam containing an open crack. The model based on Hamilton's principle and spectral analysis previously used to investigate various vibration problems, is used here to determine the effect of the excitation frequency and level of the applied forces on the dynamic response of cracked beams at large vibration amplitudes. The formulation uses "cracked beam functions", denoted as ?CBF?. These functions, which are obtained by combining the linear theory of vibration and the linear fracture mechanics theory, satisfy the natural and geometrical end conditions, as well as the inner boundary conditions at the crack location. The single mode approach is considered, which leads to simple formulae ready to use in practical engineering applications. The results obtained may be used to detect cracks in vibrating structures, via examination of the changes noticed in the non linear dynamic behaviour.