Dynamics Analysis And Fault Diagnosis Of Cracked Structures Based On The P-version FEM

Crack is one of the most common damage of engineering structures, which severely threatens the integrity and security of those structures. The vibration-based diagnosis techniques have been attracted a large number of research interest due to their prominent capabilities, such as they only depend on the global vibration signal and can be implemented in on-line manner. To identify crack parameters quantitatively, the dynamic model of structures should be established firstly and then the possible crack parameters are adjusted such that the difference between the calculated results based on the model containing crack parameters and the reference values is minimal. It can be seen that the efficiency of the dynamic model and the searching of crack parameters is crucial to the practical application of the quantitative crack identification techniques. Thus, the primary purpose of the dissertation is to present accurate and efficient dynamic models and crack identification approaches and provides a feasible scheme for on-line monitoring and diagnosis of cracks.Local flexibilities of cracks under different loading in homogeneous and non-homogeneous beams are derived firstly. Then a new methodology based on the lumped crack model and the p-version of finite element method (p-FEM) is developed to analyze the vibration characteristics and dynamic response of cracked structures. Comparisons between results by the proposed method and results in the literature and by conventional finite element method (CFEM) show that the p-FEM has superior accuracy and convergent to the CFEM. The proposed method is subsequently applied to analyze the dynamic properties of several kinds of cracked structures which have been widely used in various important engineering fields but received little attention in previous investigation, including geometrical non-uniform beams, physical non-uniform beams and rotating beams. The effect of some parameters such as crack location, crack size, boundary condition, taper ratio, material gradient and rotation speed are discussed.To avoid the accuracy loss of the rest field variables in the uni-variable finite element method, the multivariable p-FEM on the basis of the generalized variational principle and the function approximation theory is developed. The method can obtain multiple field variables simultaneously with very high precision as well as has excellent convergent, which will promote the application of structural integrity evaluation techniques with stress or strain as their inputs.As an elementary attempt, the modern immune algorithm (IA) is employed to tackle the quantitative crack identification. An improved objective function is put forward and the IA is used to solve this optimization problem. Numerical and experimental studies demonstrate that this strategy can effectively identify cracks with acceptable accuracy. This present work not only broadens the application fields of the IA, but also provides a novel way to crack detection and identification.