Crack identification of cracked beam with mode shapes and frequencies ratio contours

• Main Authors: Chih-Shiung Wang, 王志雄
• Other Authors: 李林滄
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/67211022785033027249

博士 === 國立中興大學 === 應用數學系所 === 100 === This research presents a new sectional flexibility factor to simulate the reduction of the stiffness of a single-edge open cracked beam. The structural model for crack of the beam is considered as a rotational spring which is related to the ratio of crack depth to the beam height, . The mathematical model of this single-edge open crack beam is considered as an Euler-Bernoulli beam. The modified factor, , derived in this research is in good agreement with previous researcher’s results for crack depth ratio less than 0.5. The natural frequencies and corresponding mode shapes for lateral vibration with different types of single-edge open crack beams can then be evaluated by applying this modified factor . The database of natural frequencies ratios between cracked and uncracked beams with varied cracked locations and depths are built. The two-dimensional contour maps of frequencies ratios are constructed from the database for the first three modes of a cracked beam with various crack locations and depths. The location and crack depth can be identified from the frequencies ratio contours database. The numerical model of the cracked beam can be applied as an inverse method to identify cracks in structures. Keywords: cracked beam; Sectional flexibility factor; Identification