Vibration Analysis of Circular Cylindrical Structures Using Wave Elements

• Main Authors: Ying-Yu Chen, 陳映妤
• Other Authors: Ching-Chung Yin
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/77187124677465949046

碩士 === 國立交通大學 === 工學院碩士在職專班精密與自動化工程組 === 96 === A formulation of two-dimensional wave elements for frequency equations of circular hollow structures is developed in this thesis. The standing waves appearing in a cylindrical tube comprise torsional modes, longitudinal modes, and flexural modes. The former two kinds of modes have axially symmetric motions. The exponential propagators in forward and backward axial directions are used as high order interpolation functions in each element. Flexural modes have more complicate motions and could be categorized by circumferential number n and axial mode number m. Besides the exponential propagators, flexural motions also depend on the circumferential angle through the trigonometric functions defined by n. Further calculations for resonant frequencies and modes of vibration were carried out by a commercial finite element code ANSYS with Solid 45 and Shell 63 elements. The convergence tests for resonant frequencies with respect to a variety of diameters of cylinder and axial modes were performed. In lower circumferential numbers, both elements can reach convergence in a wide range of axial mode numbers. But the converging results for higher order modes are more sensitive to the number of elements. Better convergence could be achieved by shell elements because of no meshing in thickness. The resonant frequencies of flexural vibration do not appear in sequence of the circumferential number or the axial mode number. Two non-dimensional parameters, frequency factor �� and axial wavelength factor ��, are adopted to explore the variation of resonant frequencies for flexural vibration with various numbers of n and m. Numerical results indicate that the frequency factor increases with axial wavelength factor for the circumferential number less than 2. But the proportionality might become less significant with the increase of n. The frequency factor increase monotonically with the axial mode number in the range less than 1.5. Beyond this range, it decreases first and is followed by increasing with the axial mode number.