Vibrational Power Flow Characteristics Of Cracked Structures And The Damage Detection

The work of this thesis is a part of the research project"the wave characteristics of damaged structures based on vibrational power flow and the damage detection". In this thesis, the vibrational power flow characteristics of cracked structures are researched theoretically and experimentally, and the crack detection method based on the vibrational power flow are proposed. The research enlarges the research scope of the vibration energy flow into the field of damage detection theoretically and proposes a new method to damage detection in engineering.Firstly, the modeling of cracks in the beam, plate and shell structures which often occur in engineering are investigated. Based on the fracture mechanics, the local flexibility matrix of the one-dimensional cracked structures under the coupled loads is deduced. Then the local flexibilities in a circular-section and solid rectangular-sectional beam under the bending moment are addressed respectively, by applying the least-squares method the best-fitted explicit expression of the local flexibility versus crack depth is given. The surface cracks and inner cracks in the plate and shell structures are modeled by line spring. By the transformation of three-dimensional crack issue into two-dimensional model, the local compliance of the line spring is obtained.Then the power flow characteristics of cracked Timoshenko beams and cracked thin plates are researched. The existence of the crack in the cracked structures induces the local compliance, which in turn changes the dynamic response of the cracked structures. The crack is modeled as a rational spring for beam structures and line spring for plate structures. The input power flow and transmitted power flow in cracked structures are calculated, then the relationship between the power flow characteristics and the crack information (location and depth) are discussed. The contour lines diagram of input power flow with two different driving frequencies is constructed to identify the crack, which can successfully indicate the crack's information. The sensitivity of the method is discussed.For the circular cylindrical shell structure widely used in the engineering, the vibrational power flow characteristics of thin shell with circumferential crack are investigated for the first time. The equivalent distributed line spring is designed to model the surface or inner crack in the shell. The local compliance matrix due to the presence of the crack is deduced from fracture mechanics and three modes of the crack stress intensity factors and their coupling are considered in the local compliance matrix. The vibration of the shell is descirbed by Flugge's shell equations. Under the excitation of radial harmonic line force, the input power flow and transmitted power flow of uncracked and cracked shells are obtained. The results show that the vibrational power flow of cracked shell changes substantially due to the presence of crack, and the change is strongly related to the depth and location of crack. Contours of input power flow under different frequencies are constructed to identify the location and depth of the crack.The visualization of power flow in the cracked structures are studied based on finite element method(FEM) for the first time. By introducing the concept of structural intensity(SI), the detail expressions of SI in one-dimensional, two-dimensional and three-dimensional structures are given. The streamline techque is empolyed in the visualization of SI vector field. For the elastic solid with crack, the relationship between the J integal and SI is deduced. The displacement vector plot, SI vector plot and streamline plot are obtained for different crack parameters and different dirving frequencies. The distrubition and propagation of surface energy flow in cracked structure and near the crack are given, which provides a new tool for crack detection.At last, the experimental research on the cracked cylindrical shell's input power flow is implemented. Based on sensor technology, the input power flow of cracked shell are measured. The experimental results and theoretical results show a agreement in substance, which demonstrate the accuracy of the theory and the reasonability of the experimental model's setup. The errors in the experiment are analyzed as well.