請用此 Handle URI 來引用此文件: http://hdl.handle.net/11455/17583
標題: 含 有 頂 端 質 量 之 浸 在 液 體 中 的 非 均 勻 柱 之 振 動 分 析
Vibration Analysis of Immersed Non-uniform Column Carrying A Tip Mass
作者: 吳東明
Wu, Tong-Ming
關鍵字: non-uniform column
非均勻柱
出版社: 應用數學系
摘要: 本論文探討一部份沉浸於流體中之非均勻圓柱的振動行為。吾人可用白努利-尤拉(Bernoulli-Euler)樑理論來模擬此非均勻圓柱,本論文假設在此非均勻圓柱頂端裝置有一集中質量,而在其底端則連附著平移及旋轉彈簧。吾人除了考慮外加虛擬質量在流體中對結構振動之影響外,同時亦探究此集中質量之轉動慣量及偏心矩對結構振動之效應。採用分離係數法,吾人可得此一結構系統之自然頻率及模態,在求取自然頻率的過程中,吾人須展開一 方陣之行列式,繼而使用正割法來獲致其所對應的超越函數之零根,一但吾人獲致此非均勻圓柱之自然頻率及模態後,此系統之受力振動分析即可輕易進行之。
In this study, the vibration behavior of a non-uniform circular column partially immersed in a fluid is investigated. The column is modelled as a non-uniform Bernoulli-Euler cantilever beam with a concentrated mass at the top and attached by a translational and rotational springs at the bottom. Not only we consider the effect of added virtual mass on vibration of the structure in fluid, but also we deal with the influence of rotatory inertia and eccentricity of the concentrated mass. Applying the method of separation of variables, the natural frequencies and mode shapes of the non-uniform column partially immersed in fluid can be obtained. The problem of obtaining the natural frequencies requires the expansion of an eighth order determinant, and the roots of the transcendental frequency equation are determined by using “Secant” method. Once the natural frequencies and mode shapes of the non-uniform column are calculated, the forced vibration analysis can be performed readily.
URI: http://hdl.handle.net/11455/17583
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