Natural modes of cracked beams and identification of cracks.

A method is presented for the detection and monitoring of structural cracks, based on measurements of dynamic response. The technique is to analytically model the structural dynamics based on cracked beam theories derived under the Bernoulli-Euler assumption. Crack properties (location and size of the crack) are related to the natural frequencies and mode shapes of the beam via this model. This model is incorporated into a system for the determination of crack damage through an identification process. First, an approximate Galerkin solution to the one-dimensional cracked beam theory for the free bending motion of beams with pairs of symmetric cracks is suggested. This approach provides for the determination of the natural frequencies and mode shapes of the cracked beam. To validate the computational model, a two-dimensional finite element approach is proposed, which also allows one to determine the parameter that controls the stress concentration profile near the crack-tip in the theoretical formulation. Existing cracked beam theory for a pair of symmetric cracks is extended to cover the free vibration of beams with a single edge crack. The natural frequencies and mode shapes of simply supported and cantilevered beams are computed for both symmetric and one-sided cracks. These predictions are confirmed by comparison to experimental and finite element results for both kinds of cracks. An identification procedure is developed to determine the crack characteristics from dynamic measurements. This procedure is based on minimization of either the 'mean-square' or the 'max' measure of difference between measurement data and the corresponding predictions obtained from the computational model. Necessary conditions are obtained for both formulations. The method was tested for simulated damage in the form of a simply-supported beam.PhDAerospace engineeringMechanical engineeringIndustrial engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162361/1/9001709.pd