| Summary: | 碩士 === 國立成功大學 === 機械工程學系 === 105 === In this study, the Laplace Adomian decomposition method (LADM) is used to analyze the free vibration and force vibration problems of uniform and non-uniform beams. First, to obtain the natural frequency and mode shape of the Euler-Bernoulli beam, we transformed the governing equation to the algebraic equation by LADM and used simple algebraic operations on the frequency equations afterwards. Moreover, investigating the effect of the natural frequency of the dynamic system by physical parameters including translational spring constant, rotational spring constant, taper ratio of beams and the magnitude of axial tensile. Furthermore, the LADM is applied to analyze the dynamic behavior including deformation, resonance and post-buckling of beams under the external forces.
The results of this study show that the natural frequency upper by the upper translational spring constant, the upper rotational spring constant and the upper magnitude of axial tensile. However, the upper taper ratio would make the first frequency lower and the second frequency and the third frequency upper. When resonance occurs, the very little force can still bring about the collapse of the structure. After buckling occurs, it also indicates the deflection angular upper by the upper magnitude of concentrated force and the upper angle of concentrated force.
The results of this study is consistent with analytical and numerical results given in the literature.Therefore, the LADM is simpler, faster and more straightforward than other methods.
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