DAMAGE DETECTION IN SIMPLY SUPPORTED BEAMS USING DERIVATIVES OF MODE SHAPES

摘要

It is well known that crack effects are more noticeable in the response of vibrating cracked structures when the crack depth is significant in comparison to the depth of the structure. But if the crack is relatively small, it is difficult to detect. The aim of this work is to use the derivatives of the mode shapes with respect to the space coordinates of simply supported beams to detect and locate small cracks in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small blip in the response at the crack location. Using the direct data of mode shape change, it is hard to detect small cracks in beams. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked beam are derived and investigated, they provide a progressively better indication of the presence of a crack. However, 'noise' effects due to the random variations in the response also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives. For the undamaged beam, these derivatives are smooth curves. So the local peaks or blips on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and undamaged simply supported beams used are computed using the finite element method.