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研究生:洪崇瀚
研究生(外文):Chung-HanHung
論文名稱:旋轉薄膜之動態分析與3D模擬
論文名稱(外文):Dynamic Analysis and 3D Simulation of a Spinning Thin Membrane
指導教授:莊哲男
指導教授(外文):Jer-Nan Juang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工程科學系碩博士班
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:中文
論文頁數:75
中文關鍵詞:太陽風帆旋轉薄膜系統識別
外文關鍵詞:solar sailspinning membranesystem identification
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在本論文中,我們提出一個有效率的數學模型用來分析非常長、薄且極輕的旋轉薄膜的運動行為,這種薄膜裝置被使用於Heliogyro 太陽風帆飛行器,MacNeal 在1967 年提出Heliogyro 的概念,Heliogyro 是一種太陽風帆的架構,具有數片薄膜風帆收納於中心艙體,並藉由旋轉產生的離心力將薄膜風帆從中心艙體延伸而出,薄膜風帆接受太陽光子撞擊並轉換成動量以提供太陽風帆航行所需之推進力。
本論文利用一組離散質點模擬旋轉薄膜,該離散的旋轉薄膜模型與MacNeal 所使用的連續模型不同,我們所使用的離散模型將帶來更多分析與設計控制器等優點。本論文建立的數學模型包含非線性以及線性兩大部分,非耦合的運動行為具有下述三種類型:在薄膜風帆平面上之運動、垂直於薄膜風帆平面之運動、以及扭轉運動,接著,推導垂直於薄膜風帆平面之運動與扭轉運動兩者耦合的運動方程式,利用以上四組運動方程式進行數值模擬與動態分析,藉由線性化以後的運動方程式求得旋轉薄膜的自然頻率,該自然頻率與薄膜的尺寸、質量無關,僅與旋轉速率相關,不僅如此,由離散模型求得的自然頻率與MacNeal 使用連續模型所得的自然頻率相同,最後,我們更提供立體動畫清楚地呈現旋轉薄膜的運動行為。
In this thesis, we propose a novel approach to conduct dynamic analysis of a long, thin, spinning membrane in a heliogyro solar sail. The concept of a heliogyro, first proposed by MacNeal, is a spinning solar sail architecture, which has exceeding light weight, high aspect ratio, and extremely thin membrane strips. Membrane blades are stowed in the central hub, deployed by spinning, and unrolled as well as stiffened by centrifugal force. A solar sail derives continuous thrust directly from momentum generated by solar radiation pressure.
Motions of the spinning membrane are modeled by a set of discrete lumped masses, which is different from the continuous model used in the MacNeal's equations. This gives advantages of dynamics analysis and controller design. Both nonlinear and linear equations of motion are provided to study the three uncoupled motions, in-plane motion, out-plane (bending) motion, and twisting motion. Additionally, equations of motion for coupled bending and twisting motion are derived. Numerical simulations based on equations of motion are used to study the dynamics of the spinning membrane. Natural frequencies of the linearized
spinning membrane models are independent of the geometry of the membrane, but they are related to the spinning rate of the membrane. Furthermore, natural frequencies generated
from the discrete membrane models in the thesis are identical to the ones obtained from the continuous membrane model applied in the MacNeal's equations. Three-dimensional animations are made to demonstrate both nonlinear and linear behavior of the spinning membrane.
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . ii
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Tables . . . . . . . . . . . . . . . . . . . . . vii
List of Figures . . . .. . . . . . . . . . . . . . . . . viii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Research Background and Motivation . . . . . . . . . . 1
1.2 Research Objective and Approach . . . . . . . . . . . . 2
1.3 Thesis Contribution . . . . . . . . . . . . . . . . . . 3
1.4 Thesis Organization . . . . . . . . . . . . . . . . . . 3
2 Development of Solar Sails . . .. . . . . . . . . . . . . 4
2.1 History of Solar Sails . . . . . . . . . . . . . . . . 4
2.2 Challenges of Solar Sails . . . . . . . . . . . . . . . 7
2.3 MacNeal's Equations . . . . . . . . . . . . . . . . . . 8
3 Uncoupled Motions of a Membrane . .. . . . . . . . . . . 11
3.1 Definition of a Spinning Thin Membrane Model . . . . . 11
3.2 Equations of Motion for Uncoupled Motions .. . . . . . 12
3.2.1 Pure In-plane Motion . . . . . . . . . . . . . . . . 12
3.2.2 Pure Bending Motion . . .. . . . . . . . . . . . . . 19
3.2.3 Pure Twisting Motion . . . . . . . . . . . . . . . . 24
4 Coupled Motion of a Membrane . . . . . . . . . . . . . . 31
4.1 Definition of a Spinning Thin Membrane Model . . . . . 31
4.2 Equations of Motion for a Coupled Bending and Twisting Motion . .. . . . . . . . . . . . . . . . . . . . . . . . 32
5 Numerical Simulation . . . . . . . . . . . . . . . . . . 40
5.1 Simulation of Uncoupled Motion . . . . . . . . . . . . 41
5.1.1 Pure In-plane Motion . . . . . . . . . . . . . . . . 43
5.1.2 Pure Bending Motion . . . . .. . . . . . . . . . . . 50
5.1.3 Pure Twisting Motion . . . . . . . . . . . . . . . . 53
5.2 Simulation of Coupled Motion . . . . . . . . . . . . . 56
5.2.1 Coupled Bending and Twisting Motion . .. . . . . . . 56
6 Three-Dimensional Animation . . . .. . . . . . . . . . . 61
6.1 Animation of Uncoupled Motion . . . . . . . . . . . . 62
6.1.1 Pure In-plane Motion . . . . . . . . . . . . . . . . 63
6.1.2 Pure Bending Motion . . .. . . . . . . . . . . . . . 65
6.1.3 Pure Twisting Motion . . . . . . . . . . . . . . . . 67
6.2 Animation of Coupled Motion . . .. . . . . . . . . . . 69
6.2.1 Coupled Bending and Twisting Motion . . . . . . . . 69
7 Conclusions and Future Work .. . . . . . . . . . . . . . 71
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . 71
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . 72
References . . . . . . . . . . . . . . . . . . . . . . . . 73
個人簡歷. . . . . . . . . .. . . . . . . . . . . . . . . . 75
[1] R. H. MacNeal, ``The heliogyro: An interplanetary flying machine,' tech. rep., Astro Research Corporation, March 1967.
[2] R. H. MacNeal, J. M. Hedgepeth, and H. U. Schuerch, ``Heliogyro solar sailer summary report,' tech. rep., National Aeronautics and Space Administration, Washington, D.C., June 1969.
[3] R. H. MacNeal, ``Structural dynamics of the heliogyro,' tech. rep., National Aeronautics and Space Administration, Washington, D.C., May 1971.
[4] J.-N. Juang, C.-H. Hung, and W. K. Wilkie, ``Dynamics of a slender spinning membrane,' in Jer-Nan Juang's Astrodynamics Symposium, June 2012.
[5] W. K. Wilkie, J. E. Warren, M. W. Thompson, P. D. Lisman, P. E. Walkemeyer, D. V. Guerrant, and D. A. Lawrence, ``The heliogyro reloaded,' tech. rep., NASA Langley Research Center, December 2011.
[6] L. Johnson, M. Whorton, A. Heaton, R. Pinson, G. Laue, and C. Adams, ``Nanosail-d: A solar sail demonstration mission,' Acta Astronautica, vol. 68, pp. 571--575, 2011.
[7] M. Macdonald and C. McInnes, ``Solar sail mission applications and future advancement,' in 2nd International Symposium on Solar Sailing, July 2010.
[8] R. F. Crawford, J. M. Hedgepeth, and P. K. Preiswerk, ``Spoked wheels to deploy large surfaces in space - weight estimates for solar arrays,' tech. rep., National Aeronautics and Space Administration, Washington, D.C., January 1975.
[9] D. V. Guerrant, D. A. Lawrence, and W. K. Wilkie, ``Dynamics and control of the heliogyro solar sail demonstrator,' in 63rd International Astronautical Congress, October 2012.
[10] R. S. Blomquist, Heliogyro Control. PhD thesis, The Robotics Institute, Carnegie Mellon University, April 2009.
[11] J.-N. Juang and M. Q. Phan, Identification and control of mechanical systems. Cambridge University Press, November 2006.
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