A Study Of Flexibility Curvature Matrix For Structural Damage Identification

The main research contents of structural damage identification are to determine the structure of health status through tested various engineering structures and appropriately analysis these tested results. It deals with the damage which is in the internal structure or invisible with the naked eye. Detection methods often require non-destructive and recognition results will be an important basis as safe use and maintenance of the structure. There are three key questions to solute in various identification methods: 1) whether the damage is existence in the structure; 2) to determine the damage location of the structure; 3) to confirm the damage degree or damage form. Damage identification has important engineering background, the research concern aerospace, transportation, architecture, and many other fields. It is also a class of typical inverse problem in mechanics and engineering, the inverse problem in engineering is to be determined the anti-multiple unknown functions, namely, the anti-types inverse problem may appear at the same time in one practical problem. In order to simplify the solving or make it possible to solve, regard being determined or considered functions as known in commonly used methods, first decomposition of the difficulties, and then gradually solved. So damage identification also has theoretical significance.Damage generally produces changes in the structural physical properties (i.e., stiffness, mass, and damping), and these changes are accompanied by changes in the modal characteristics of the structure (i.e., natural frequencies, mode shapes, and modal damping). This phenomenon has been widely noted and used by structural engineers for detecting damage or health monitoring of a structure. Therefore, the study of structural vibration test data for structural damage identification has received much attention by many researchers. Some researchers used modal flexibility changes to identify structural damage, discovered and pointed out that the modal flexibility is more sensitive to local damage than the natural frequency or mode shape and thought that it can be well used to identify structural damage.Flexibility matrix can be more accurately obtained by the first few natural frequencies and modal shape through the tested data from the structure. According to vibration theory, for many degrees of freedom systems, the flexibility matrix is obtained by reciprocal relations between flexibility matrix and stiffness matrix. Flexibility matrix elements inverse ratio square of the natural frequencies, that is, low-vibration mode and frequency in the flexibility matrix has a great impact. The lowest few modes and frequency can only be measured in practical applications and the flexibility matrix can be approximately obtained through these tested data. In the algorithm for damage identification using of the structure stiffness matrix, the approximate error is large with modal stiffness matrix which is obtained by limited low-level modal information, but flexibility matrix can be avoided this shortcoming.Proposed plate structural damage identification theory based on flexibility curvature. Derived flexibility curvature formula of two-dimensional structure, and the damage index of plate based on these formula, namely flexibility curvature matrix. The theory can determine whether the damage is existence in plate structure and confirm the damage location at the same time. Equivalent curvature ratio is defined and regression the discriminating formula about degree of damage through simulation. Simulation analysis showed that the method can well determine the damage location and degree of damage.Through the plate structure theory developed the stiffened panel structural damage identification theory based on flexibility curvature. Firstly, plate of stiffened panel is identified. Secondly, the tendon of stiffened panel is identified. The damage location can be determined by the figures of flexibility curvature matrix about damaged structure or by the rows or columns of flexibility curvature matrix. A few important matrices as damage indices are given through simulation experiments. Verified and optimized the theory by these index matrices. The damage identification process of the stiffened panel structure is given at the same time.The cylindrical structure damage identification theory based on the flexibility curvature is set up. The tubular structure analysis method and judging criteria which is based on the flexibility curvature is proposed. Firstly, the damage index of flexibility matrix is obtained, and then analysis the axial and circumferential flexibility curvature. Consider structure using the theory of chapter two in axial direction to obtain the flexibility curvature matrix. Circumferential flexibility curvature matrix can be obtained by circular curvature. The damage can be well determined through the axial or circumferential flexibility curvature matrix. The flexibility curvature matrix about both displacement and rotation can detect the damage well in the simulation analysis. Equivalent curvature ratio is defined, the curve of ECR-SD is given and regression the discriminating formula about degree of damage through much simulation. The location of damage can be analysis by index matrix and the degree of damage can be analysis by the damage coordinates and equivalent curvature ratio.Modal experiment of simply supported plate with opposite edges and simply supported plate with three edges is carried out. The mode and natural frequency of these two plates are obtained. SISO modal experiment and pure modal experiment are carried out with simply supported plate with three edges. SISO modal experiment is carried out with simply supported plate with three edges. The theory which is proposed is verified through the damage identification by the data from the experiments. The results of experiment are not better than the simulation experiments, but they can also detect the damage. The results of pure modal experiment are better than others.Damage identification usually used the modal information from the structure before damage. For mechanical engineering, marine engineering, marine platforms and other large engineering structures, it is not economic to backup mode information after completion, because these need many resources. So the technology is more important with no original modal parameters to identify damage. The above methods are built up based on curvature of flexibility, they do not need original structure data and only need low modal information to make damage detection. All of them have two advantages: 1) less calculation amount and simple execution; 2) Modal flexibility can be obtained from static or dynamic method, or be integrated in two ways.