Vibratory Characteristics, Stability Analysis And Damage Detection Of Discontinuous Beams

The discontinuous beams and columns as specific elements of structures have widerange of applications in various machines, aircraft and aerospace structures. Theconnotative meaning of discontinuity is, one or a few of deflection, rotation, bendingmoment and shear force has jumped discontinue points. The requirement ofdiscontinuous beams is not merely for assuring the structural efficiency or noise andvibration reduction of structures but is also motivated by the damage conditionsappearing in beams. Therefore, vibratory characteristics and buckling analysis ofdiscontinuous beams are great significance for maintaining safety and integrity ofstructures and avoiding loss due to the catastrophic failure of structures.This thesis deals with the free vibration and stability problem as well as damagedetection of beams with arbitrary discontinuities under different boundary conditions.The thesis mainly contains following contents:First, a critical overview of the vibration analysis methods (such as theRayleigh-Ritz method, the assumed modes method of traditional approaches, thenumerical assembly method, the transfer matrix method, the dynamic stiffness methodand the generalized function method, etc.) for discontinuation beams are presented.Then a brief review for the vibration-based damage detection methods are presented.Second, a vibration analysis model of arbitrary discontinuous beams based ongeneralized functions is established. The general governing differential equations of thevibration of Euler-Bernoulli beams with arbitrary discontinuities subjected to axial forceand/or elastic foundation are presented by introducing the discontinuity point usinggeneralized functions. The equation is then solved based on Laplace transformation.Unlike the classical solutions of discontinuous beams, the proposed scheme is valid inarbitrary miscellaneous discontinuities conditions, the generalized solutions can beexpressed in the terms of a single expression on the entire beam. As the specifieddiscontinuities type, eigenvalue matrices are simplified by the degenerated continuityconditions. The accuracy and efficiency of the proposed method are verified withseveral numerical examples and compared with published results.Third, the proposed method is extended to analyze the stability and buckling ofdiscontinuous beams. To investigate the effects of the location, depth, quantity and number of cracks on buckling, a parametric study is carried out and discussed indifferent condition cases.Final, the modal curvature change index based damage detection method isestablished using the proposed approach. Theoretical model of the auxiliary mass baseddamage identification method is also established. Then the fractal dimension method isimposed to analyze the natural frequency curve, and the location and depth of the crackcan be detected. The simulation results demonstrate that these two damage detectionmethods perform fair enough. Furthermore, the auxiliary mass based method does notneed the intact and/or damaged structure’s mode shape information, it means that theauxiliary mass based damage identification method could be operated in an ambientexcitation environment and real-time monitoring.