Damage Detection Research In Periodically-supported Structures Based On The Frequency Sensitivity-based Approach

The damage detection methods based on vibration mainly divided into model methods based on dynamic model and modelless methods based on signal analysis.The modelless methods usually only determine where the damage occurs,while the model dynamic detection methods can simultaneously determine the damage site and assess the degree of damage,damage detection based on sensitivity analysis is one of the most important categories and is widely concerned.The sensitivity analysis method in structural damage detection is based on the analysis and calculation of the sensitivity of the natural modal parameters to the structural parameters to determine whether the structure is damaged and determine the damage position and its degree.The key to this method is to select the parameters that are measurable and sensitive to structural damage.The detection parameters including natural frequency,the modal shape and the curvature of modal shape are more widely reported.The above studies were all based on the modal parameter sensitivity coefficient obtained from the parameters of the health model,when the structural parameters can not be obtained,these methods will be limited.Supported by the the National Natural Science Foundation of China(No.51208390),a damage detection methodology for large periodically-supported structures based on sensitivity analysis of modal parameters has been developed in this thesis,combining wave propagation principle and characteristic receptance method.The specific research contents are as follows:(1)Based on an infinite mono-coupled periodic system,this paper analyzes its free wave propagation law by using wave propagation theory and gains the interrelationship between the wave propagation constant and the receptances.then,this system is further extended to a finite mono-coupled periodic system of N elements with a single disorder.The characteristic equation of natural frequencies of the mono-coupled periodic system is obtained which can reflect the relationship between the change of natural frequencies and the change of element stiffness before and after damage.(2)On the basis of the above theory,a concept of non-dimensional natural frequency is proposed by analyzing the free vibration of a finite periodically-supported structure of N elements with a single disorder based on the wave propagation method.In addition,the relationship between the change of non-dimensional natural frequencies and the change of cell element overall stiffness before and after damage is obtained.And then,the modal sensitivity coefficients of the non-dimensional naftural frequencies with respect to the change in element stiffness is introduced combined by using the concept of sensitivity.The damage scenarios in large periodically-supported structures are identified by establishing a set of underdetermined equations based on the sensitivity matrix of the non-dimensional natural frequencies with respect to the change in element stiffness and solving it with constraint optimization method.(3)The proposed method is demonstrated with two numerical case studies and an experimental case studies by utilizing only the frequency measurements for the first few modes before and after damage.Among the two numerical case studies,one is the periodically-supported beam which considers the overall stiffness reduction of the cell and the other is the periodically-supported flanged pipeline which considers only the local stiffness reduction of the cell and the effect of additional quality.The experimental case studies conducted for a periodically-supported beam with various damage scenarios.Furthermore,the damage detection method proposed in this paper is independent of the structural geometric and material parameters such as mass density,elastic modulus,structural length and cross-sectional shape,size,which indicates that this method will have significant advantages and practicality.