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研究生:林忠義
研究生(外文):Chung-Yi Lin
論文名稱:含拘束阻尼層旋轉預扭樑系統之振動與穩定性
論文名稱(外文):Vibration and Stability of Rotating Pre-twisted Beam Systems with a Constrained Damping Layer
指導教授:陳聯文
指導教授(外文):Lien-Wen Chen
學位類別:博士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:147
中文關鍵詞:動態穩定旋轉預扭樑拘束阻尼層
外文關鍵詞:constrained damping layerdynamic stabilityrotating pre-twisted beam
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本文使用有限元素法,研究各種受軸向力或隨動力作用,貼覆被動型或智慧型拘束阻尼層旋轉預扭樑系統之振動與穩定性問題。本文使用黏彈材料當作阻尼層,並且使用複數模數表示黏彈材料之剪力模數。而在動態穩定性問題方面,將修改Bolotin的方法,使其可以用在本文的模型上。
在貼覆被動型拘束阻尼層旋轉預扭葉片方面,首先推導承受軸向力或隨動力作用之旋轉預扭葉片的運動方程式,其次探討在軸向力或隨動力作用下之各式旋轉預扭三明治葉片系統的靜態與動態穩定性。結果顯示,當葉片旋轉時,三明治葉片系統自然頻率比純葉片大。在受縱向力作用時,三明治葉片系統之臨界負荷要比純葉片高,而且三明治葉片系統在由隨動力所產生之不穩定,其第一與第二自然頻率並不相等。而預扭角使得旋轉預扭三明治葉片系統阻尼降低。
在貼覆被動型拘束阻尼層自旋預扭樑方面,首先推導承受軸向力或隨動力作用之旋轉預扭樑的迴動速度方程式,其次探討自旋預扭三明治樑系統的臨界轉速與在軸向力或隨動力作用下之各式穩定性。研究中發現,當三明治樑系統旋轉時,其臨界轉速比純樑低。而當自旋預扭三明治樑系統承受縱向力作用時,其穩定性比純葉片佳,而且自旋預扭三明治樑系統在由隨動力所產生之顫振不穩定,其第一與第二自然頻率並不相等。而預扭角使得自旋預扭三明治樑系統阻尼增加。
最後本文將討論貼覆智慧型拘束層阻尼之旋轉預扭葉片系統的振動與穩定性問題,智慧型拘束層阻尼的設計,主要是由壓電感知器與致動器把黏彈層夾在中間所組成,把這種裝置貼覆在振動的結構上,就可以當作一種智慧裝置。這種結構可以藉由壓電感知層量測結構的振動響應,並且使用回饋控制器來調整壓電致動器的軸向變形,因此可以在結構上提供可調整而且足夠的阻尼。本文使用比例微分控制器來調整壓電致動器的電壓,而從研究中發現,使用智慧拘束阻尼層之旋轉葉片系統,可以藉由調整比例微分控制增益獲得更佳的系統性能。
The objective of this dissertation is to study the vibration and stability problems of rotating pre-twisted beam systems with passive or smart constrained damping layer subjected, respectively, to axial and follower forces by using the finite element method. The complex modulus is used for the viscoelastic material. In the dynamic stability problems, the regions of instability are determined by using Bolotin’s procedure, modified for the complex case.
In the passive constrained layer damping (PCLD) treatments, two models, the rotating pre-twisted sandwich blade and the spinning pre-twisted sandwich beam, are studied. The equations of motion of rotating pre-twisted sandwich blades or spinning pre-twisted beams subjected, respectively, to axial and follower forces are derived by Hamilton’s principle. The vibration and stability behavior of the rotating system with PCLD treatment are discussed and compared with no damping treatment. The results reveal that rotating systems with the PCLD treatment subjected to longitudinal forces are more stable than that without damping treatment. The dynamic instability problem of rotating systems subjected to follower forces is also studied. For the rotating system with a PCLD treatment, as the flutter instability occurs, the first and second natural frequencies are not equal. The amplitude at the resonance is reduced as rotating beam systems with a PCLD treatment. The effect of pre-twisted angle on the system damping is detrimental for rotating pre-twisted sandwich blade systems, but it is beneficial for spinning pre-twisted sandwich beam systems.
In the smart constrained layer damping (SCLD) treatments, the vibration and stability behavior of rotating pre-twisted blade systems with a smart constrained layer damping (SCLD) treatment are studied. The SCLD design consists of viscoelastic shear layer sandwiched between a piezoelectric sensor and a piezoelectric actuator. This composite SCLD when bounded to a vibrating structure acts as a smart treatment. The piezoelectric sensor layer measures the vibration response of the structure and a feedback controller is provided that regulates the axial deformation of the piezoelectric actuator, thereby provide adjustable and significant damping in the structure. The proportional and derivative controller (PD controller) is used to study the effect of the SCLD on the vibration suppression performance and stability behavior. The PCLD systems could be obtained as the controller is closed. The results show that SCLD systems have better stability and vibration suppression performance by regulating the proportional and derivative gains.
摘 要i
Abstractii
符號說明iv
表目錄viii
圖目錄ix
第一章緒 論1
1-1 研究背景1
1-2文獻回顧2
1-3本文架構6
第二章預扭三明治樑之振動與穩定性分析8
2-1 有限元素模型8
2-2 運動方程式10
2-3 邊界條件13
2-4 數值結果與討論14
2-5 結論16
第三章旋轉預扭三明治葉片之振動與穩定性分析29
3-1 運動方程式29
3-1-1 動能29
3-1-2 離心力所作的功30
3-1-3 運動方程式31
3-2 穩定性分析31
3-3 數值結果與討論32
3-3-1 縱向力作用下的穩定性32
3-3-2 振動分析34
3-4 結論35
第四章旋轉預扭三明治葉片之動態穩定性分析48
4-1 運動方程式48
4-2 邊界頻率方程式48
4-3 數值結果與討論50
4-4 結論53
第五章自旋預扭三明治樑之振動與穩定性分析73
5-1 迴轉運動方程式73
5-2 穩定性分析74
5-3 數值結果與討論75
5-3-1 臨界速度分析76
5-3-2 縱向力作用下的穩定性77
5-3-3 振動分析78
5-4 結論79
第六章自旋預扭三明治樑的動態穩定性分析98
6-1 邊界頻率方程式98
6-2 數值結果與討論98
6-3 結論101
第七章貼覆智慧型拘束阻尼層旋轉預扭葉片之振動與穩定性分析120
7-1 智慧型拘束層阻尼120
7-1-1 感知方程式120
7-1-2 比例微分控制器121
7-1-3 主動阻尼121
7-2 運動方程式122
7-3 數值結果與討論123
7-3-1 振動分析123
7-3-2 穩定性分析124
7-4 結論124
第八章結論與建議135
8-1 綜合結論135
8-2 未來研究方向與建議136
參考文獻137
自述147
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