MODAL-ANALYSIS OF A CRACKED BEAM

This paper addresses the problem of vibrations of a cracked beam. In g eneral, the motion of such a beam can be very complex. This phenomenon can be attributed to the presence of the non-linearity due to the ope ning and closing of cracks. The focus of this paper is the modal analy sis of a cantilever beam with a transverse edge crack. The non-lineari ty mentioned above has been modelled as a piecewise-linear system. In an attempt to define effective natural frequencies for this piecewise- linear system, the idea of a ''bilinear frequency'' is utilized. The b ilinear frequency is obtained by computing the associated frequencies of each of the linear pieces of the piecewise-linear system. The finit e element method is used to obtain the natural frequencies in each lin ear region. In order better to understand the essential non-linear dyn amics of the cracked beam, a piecewise-linear two-degree-of-freedom mo del is studied. Perturbation methods are used to obtain the non-linear normal modes of vibration and the associated period of the motion. Re sults of this piecewise-linear model problem are shown to justify the definition of the bilinear frequency as the effective natural frequenc y. It is therefore expected that calculating piecewise mode shapes and bilinear frequencies is useful for understanding the dynamics of the infinite degree of freedom cracked beam. (C) 1997 Academic Press Limit ed.