A study of Vibrations of Spatially Curved Beam by using Finite Element Method

• Main Authors: Tiao-Yu Chen, 陳調裕
• Other Authors: Dr.Yaw-Dong Shih
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/66862555276572995566

碩士 === 大同大學 === 機械工程研究所 === 89 === In this thesis, the vibrations of spatially curved and twisted beams of square cross-section. Every sliced element of the beams along the centerline of beams has three translational displacements and three rotational degrees of freedom. First of all, the displacement functions are employed to describe the dynamic equilibrium of the curved and twisted beams, and the relations of linear strain-displacement are employed to establish the governing equations. The time dependency in the displacement functions is assumed in exponential form. The six governing equations are simplified to a time-independence formulation. Considering the restriction of boundary conditions, a Finite Element Method is used to solve the eigenvalue problem for the natural frequencies. The effects of the curvature and torsion, which are on the natural frequencies of the curved and twisted beams, are studies in the geometrically permissible region. In order to obtain an accurate solution, besides the original system, the eigenvalue of its associate adjoint system is calculated in the meantime. As a result, the error between these two eigenvalues is less than 10-5 when the number of element for Finite Element Method is greater than 50. When the curvature and torsion are zero to solve the leading four natural frequencies. Then, it was compared that can be divided them variables in five types (T=0.0K, T=0.5K, T=1.0K, T=1.5K, and T=2.0K). The result shows that all five types of the first natural frequencies of the curved and twisted beam decrease as either the value of torsion and curvature increase in general. In addition to this, also it is analysis that the rate of length and width of leading four natural frequencies. As a result, there is a decrease in the number of leading four natural frequencies of beam; there is an increase in the rate of the length of the beam. Finally, it was used that the natural frequencies of curved and twisted beam, also it can be obtained that the displacement function graph of three translational displacements and three rotational angles of curved and twisted beam.