Damage Diagnosis Based On Flexibility Matrix Under Environmental Excitation

Aiming at the problem of the un-mass normalization of the modal shapes measured under environmental excitation,this paper conducts a detailed study on the mass normalization factor based on the mass change method,and two methods for solving the mass normalization factor(based on the sensitivity of the modal parameters and the method based on the classical vibration equation)are deduced and compared,the difference and relationship between the two are revealed,and the optimal formula for solving the mass normalization factor is proposed.In order to realize the purpose of identifying structural damage under environmental excitation,several damage diagnosis methods based on modal flexibility matrix under environmental excitation are proposed.Main research content:(1)The method of mass normalization for the shape is deduced and studied,and the connection and difference between the two mass normalization formulas based on the additional mass method are revealed through numerical examples,and the study shows that the normalization factor approximation formula based on the modal parameter sensitivity method is only a special case of the formula based on the classical vibration equation method.The relationship between the error sizes of the three calculated mass normalization formulas derived based on the equation of motion method in various modes of vibration patterns is also investigated,and the optimal distribution law of the additional mass is explored.(2)The existing flexibility damage detection method is improved appropriately,and a new damage localization index is proposed by introducing the curvature formula,and the numerical example verifies its feasibility,which is more robust and intuitive than the traditional flexibility matrix-based damage index.Considering the influence of the measured degrees of freedom of the structure incomplete,the flexibility matrix based on modal reduction was further deduced,and the derivation ideas of the new damage localization index were applied to the flexibility matrix based on modal reduction,and the corresponding damage localization index is obtained,so as to realize the damage identification of the structure with incomplete degrees of freedom,and the case study showed that the proposed new localization index is more robust and intuitive.It still has a high noise resistance after the modal reduction.(3)This paper studies the influence of the modal flexibility matrix on the accuracy of structural damage recognition under different matrix decomposition methods(LU decomposition and QR decomposition),After decomposition,the triangular matrix(U matrix and R matrix)is used as The research object,the damage location index based on a triangular matrix is proposed,and verifies its accuracy and robustness through calculation examples.The research work in this thesis provides a theoretical basis for the processing of un-mass normalized mode shapes under environmental excitation,provides new ideas for damage diagnosis under environmental excitation,and also provides structural damage diagnosis methods for incomplete measured degrees of freedom Reference.