| Summary: | 碩士 === 大同大學 === 機械工程研究所 === 88 === In this thesis, the vibrations of spatially curved and twisted beams of square cross section are discussed. Every sliced element of the rod has three translational and three rotational angles along the centerline of beams. Now these displacement functions are used to describe the dynamic equilibrium of the curved and twisted beam and the relations of linear strain-displacement are used to establish the governing equations.
The time dependency in the displacement functions is assumed in exponential form, the governing equations are then simplified to a time-independence formulation. Considering the restriction of boundary conditions, we assume the appropriate approximate solutions of the displacement functions and rotation functions as Fourier sine series Galerkin method are used to solve the eigen value problem for the computation of the natural frequencies. The effects of the curvature and torsion on the natural frequencies of the spatially curved and twisted beam are studied.
By the numerical computation, the four leading natural frequencies for various curvature and torsion are obtained. When curvature and torsion is zero, the natural frequencies for every vibration mode are single valued. As the torsion and curvature and torsion, the vibration mode of natural frequencies will split into two branches.
For small curvature and torsion, there are two frequencies splitted. One is the natural frequency of in-plane vibration, and the other is natural frequency of out-plane vibration. For curvature and torsion become large, the out-plane vibration will change to a normal-dominate vibrations, and the in-plane natural vibration will change to a by-normal-dominate vibrations.
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