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

Abstract

The beam structure is widely used in engineering structures and plays an important role in large mechanical structures. A crack is one of the main causes of the failure of the beam. In order to locate the position and identify the degree of the 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 a database of the ratio parameters for crack locating. Combined with the database, crack position criteria are proposed. The region where the 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 accurately in the regions. To identify the degree of the crack, a crack degree parameter, 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 the crack is established. Through the correlation, the degree of the crack can be ascertained after crack location. For thin-walled cantilever beams, such as wind turbine blades and aircraft wings, the natural frequency variation caused by the 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 a 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.