Crack diagnosis method for a cantilevered beam structure based on modal parameters

Beam structure is widely used in engineering structure and plays an important role in large mechanical structure. Crack is one of the main causes of the failure of beam. In order to locate the position and identify the degree of crack more accurately, a new crack diagnosis method is proposed in this paper. It is found that the ratio of the adjacent two-order natural frequency variation is related to the crack position alone. Based on the ratio parameters, the beam is virtually divided into a number of connected regions. The crack is implanted into each joint point of regions to establish the database of the ratio parameters for crack locating. Combined with the database, a crack position criteria are proposed. The region where crack exists can be ascertained. Then, a new position parameter in the region is proposed, and the mapping between this parameter and the detail position within the region is established. The crack can be located more accurate in the regions. To identify the degree of crack, a parameter of crack degree, which is defined as the ratio of the variation of the natural frequency to the natural frequency itself, is proposed. Based on simulation and data analysis, the correlation between the parameter and the degree of crack is established. Through the correlation, the degree of crack can be ascertained after crack locating. For thin walled cantilever beams, such as wind turbine blades and aircraft wings, the natural frequency variation caused by crack will be more obvious. The above proposed crack diagnosis method will be more effective in this case. The numerical simulation analysis and test results for cantilevered thin walled beam with different cross-sectional shapes are compared with those of theoretical results, and the results show that the proposed method for crack diagnosis is effective and accurate.

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