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研究生:楊金生
研究生(外文):Chin-Sheng Yang
論文名稱:彈性拘束且具附著物之旋轉非均勻Timoshenko樑的彎曲振動
論文名稱(外文):Bending vibrations for an elastically restrained rotating non- uniform Timoshenko beam with attachments
指導教授:李森墉
指導教授(外文):Sen-Yung Lee
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:1993
畢業學年度:81
語文別:中文
論文頁數:39
中文關鍵詞:安置角錐度比壓力挫曲臨界旋轉角速度
外文關鍵詞:setting angletaper ratiocompression bucklingcritical rotating speed
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本文利用Hamilton原理,針對具附著物之旋轉非均勻Timoshenko樑的的彎
曲振動問題。將非均勻Timoshenko樑兩個偶合的統御微分方程式,減化成
一個完全由彎曲造成之旋轉角度或撓曲位移表示的四階統御微分方程式。
找到彎曲角度和撓曲位移間的明顯關係式。其頻率方程式可利用減化後之
統御方程式的四個正規化基本解表示之。如果樑的幾何,材料性質可以表
示為多項式,則可利用Frobenius 法得到確切解。第一,當旋轉樑長度小
於剛性環迴旋半徑由於樑承受離心力造成的壓力,可找出安置角度、錐度
比與彈性拘束對自然振動頻率的影響。第二,探討旋轉非均勻Timo-
shenko樑在不同樑長度下,所產生挫曲的臨界旋轉角速度之影響。第三,
研討不同附著物質量變化對旋轉非均勻樑自然振動頻率的影響。第四,探
討旋轉非均勻Timoshenko樑端軸差變化與附著物質量變化時,安置角對自
然振動頻率之影響。當旋轉樑的根部軸心端時,樑承受離心力所造成的張
力。如果樑長度小於迴旋半徑且旋轉樑的根部在遠離軸心處時,樑承受離
心力所造成的壓力。如果樑長度大於迴旋半徑時樑部份承受壓力,部份承
受張力。承受壓力的旋轉樑之現有的研究僅限於均勻Bernoulli-Euler 樑
。當無因次端軸差r小於零時,欲使樑產生挫曲則須提高旋轉速度,而且
樑安置角不同,臨界角速度差異頗大。無因次附著物質量愈大,自然振動
頻率下降較快。尤其當r大於零,旋轉樑由於離心力造成全部壓力,附著
物質量增加更加速自然振動頻率下降,而且樑安置角不同,臨界角速度差
異不明顯。

By the theorem of Hamilton to the problem of bending vibra-
tions for an elastically restrained rotating nonuniform
Timo- shenko beam with attachments in this paper,the coupled
differen- tial governing equations of an nonuniform
Timoshenko beam are reduced into two complete forth-order
differential governing eq- uations with variable coefficients
in the flexural displacement or in the angle of rotation due
to bending ,respectively.The ex- plicit relation between the
flexural displacement and the angle of rotation due to bending
is established . The frequency equa- tions of the beam with a
general elastically restrained root are derived and expressed
in terms of the four normalized fundamen- tal solutions of the
associated governing differential equations . Consequently ,if
the geometric and material properties of the beam are in
polynomial form ,then by the method of Frobenius the exact
solution for the problem can be obtained. First, considering
the dimensionless length of a rotating beam shorter than the
radius of the rigid ring , as the rotating beam in all
compression due to the centrifugal force , it is ob- served
that setting angle , taper ratio and elastic constraint have
the influence on the natural frequencies. Second, an
nonuniform Timoshenko beam with the variance of length of
the rotating beam has the influence on the critical rotating
speed.Third,the variance of the tip mass given on which end of
a rotating nonuniform beam , it has the influence on the
natural frequencies. Finally, a rotating beam clamped at the
ri- gid ring which radius is shorter than the length of the
beam is partly in compression and partly in tension. Until now
only con- sidered , a uniform Bernoulli-Euler beam that clamped
at the ri- gid ring has a constant setting angle and rotating
speed.

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