Damage Identification Of Euler-Bernoulli Functionally Graded Beam Structures By Modal Strain Energy Method

Functionally graded materials (FGMs) are a new kind of heterogeneous composite materials that natures of the material and function change continuously and gradiently as the space. FGMs are widely used in many fields due to their unique feature. The damage may appear in the FGM structures because of a variety of reasons, which will lead to structural failure and have a direct impact on people’s life safety, the national economy and social stability. Therefore, it is necessary to have a research on the damage identification of the FGM structures.According to the finite element formulation available in published literature, the frequency eigenvalue and the modal mode of Euler-Bernoulli functionally graded beams (FGBs) are calculated through the computing platform of the finite element method commercial software ABAQUS. This work lays a foundation for the damage identification of Euler-Bernoulli FGB structures.Based on the modal strain energy change ratio method (MSECRM), the element damage location index (EDLI) damage is given. The locations of one damaged element and two damaged elements are identified by the given index respectively. In regard to the influences of the material graded variation index and the boundary conditions of Euler-Bernoulli FGBs on the identified results, this paper discusses them fully. Numerical examples show that the identified results for the element damage locations have high accuracy, have no disturbed element and are not affected by boundary conditions. The proposed index for Euler-Bernoulli FGB structures has higher sensitivity. On the basis of the above identified locations of the damaged elements, the element damage degree index (EDDI) is given by the modal strain energy method (MSEM). The EDDI is employed to identify the damage degrees of one damaged element and two damaged elements respectively under the different material graded variation index and boundary conditions of Euler-Bernoulli FGBs. Numerical examples reveal that the identified results for the element damage degrees have high precision and are not affected by boundary conditions.