| Summary: | 碩士 === 中原大學 === 機械工程研究所 === 89 ===
A small deformation vibration of a cantilever cracked shaft under alternating torsional moment、bending moment、shear force and uniform load is considered. Including torsional moment、bending moment、shear force and uniform load, the equations of motion and boundary conditions are derived by Hamilton’s principle. Mathieu equation is derived by Galerkin’s method. Using Runge-Kutta method, the relation between amplitude and loading cycles is determined. The modified Forman model is applied to calculate the crack growth. Using K-effect, Combining the different stress intensity factors (SIF) of crack mode. Several cases of vibration with torsional moment、bending moment and shear force applied on the shaft are considered, and the interaction between vibration and fatigue is discussed in this study. Combining the analysis of vibration and fatigue can describe the phenomenon of fatigue crack growth more realistically. When the dynamic instability occurs, the crack grows fastly and the life of fatigue reduces. The results show that the fatigue and vibration are obviously interactive.
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