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研究生:吳兆平
研究生(外文):Chao-Ping Wu
論文名稱:細長撓性體波動推進之運動模擬
論文名稱(外文):Simulation on the Undulatory Locomotion of a Flexible Slender Body
指導教授:邱逢琛邱逢琛引用關係郭振華郭振華引用關係
指導教授(外文):Forng-Chen ChiuJenhwa Guo
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:造船及海洋工程學研究所
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:2000
畢業學年度:88
語文別:英文
論文頁數:42
中文關鍵詞:仿生波動的運動推進水下載具魚形鰻魚
外文關鍵詞:biomimeticundulatorylocomotionpropulsionunderwater vehiclefish-likeeel
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在海洋科學與工程應用的領域上,無人水下載具的研發已經進步到了一個載具能夠提供特殊潛能的重要轉捩點。為了探討於低速運動時具更佳操縱性表現與更高效率、藉由擺動推進的仿生型自主式水下載具的發展可能,以細長撓性體的波動推進來做運動模擬是極有幫助的。
本文中,當分成數段的細長撓性體在波動時,隨著由頭傳向尾的波動,每一段素因動量的改變以及摩擦力的作用所引起的反作用力都將列入考慮。藉由分別相加各段素的軸向、側向作用力與偏搖力矩可得到物體固定座標系所描述的運動方程式,並以時間積分法隨著時間軸逐步求解得到各時刻的速度。將物體固定座標系所描述的速度轉換到空間固定座標系後,就可輕易地經由對轉換後的速度做時間積分而得到物體的運動軌跡。
這個細長撓性體波動推進模擬的理論將會運用在一些魚形和鰻形的運動實例上;將所表現出來的特性與現存的資料相比較,並藉此討論此模擬方法的適用性與限制。
The technology in connection with the development of unmanned underwater vehicles has advanced to the point where such vehicles now offer a potential for significant improvements in ocean science and engineering applications. In order to develop a biomimetic undersea vehicle propelled by the undulatory motion of a flexible hull, which may has a better performance in control and more efficiency in slow motion, it would be helpful to simulate the locomotion by the undulatory motion of a flexible body.
In this paper, when the flexible slender body which is divided into a number of segments undulates, the wave passes from the nose to the tail, the reaction forces due to momentum change, friction as well as cross flow drag acting on each segment are taken into account. Equations of motion described by the body-fixed coordinate are obtained by taking the summation of the longitudinal force, lateral force and yaw moment acting on all the segments, respectively. Equations of motion are solved step by step in time axis and the velocity is transferred to space-fixed coordinate. Then the trajectory of the flexible body can be obtained easily just by time integration of the transferred velocity.
Some cases of eel-like locomotion as well as fish-like locomotion will be studied by simulation to show their characteristics and compared with existing data. The validity and limitation of the present simulation method will be discussed.
1. INTRODUCTION………………………………………………………………1
1-1. Motivation………………………………………………………………1
1-2. Review and background ………………………………………………1
2. GOVERNING EQUATIONS ……………………………………………………4
2-1. Coordinate systems……………………………………………………4
2-2. Wave equation …………………………………………………………4
2-3. Simulating the undulation of a flexible slender body………5
2-4. Motion equations in the body-fixed coordinate system………6
2-5. Newmark-β method……………………………………………………10
2-6. Transfer between coordinate systems of the horizontal velocity………………………………………………………………………12
2-7. The trajectory of the body ………………………………………12
3. NUMERICAL SIMULATION …………………………………………………13
3-1. Program description…………………………………………………13
3-2. Added artificial springs …………………………………………14
4. SIMULATION CASES ………………………………………………………16
4-1. Case 1 …………………………………………………………………16
4-2. Case 2 …………………………………………………………………23
4-3. Discussions……………………………………………………………28
5. CONCLUSION ………………………………………………………………30
REFERENCES……………………………………………………………………31
APPENDIX 1……………………………………………………………………32
APPENDIX 2……………………………………………………………………33
APPENDIX 3……………………………………………………………………42
[1] Lighthill, M. J., Mathematical Biofluiddynamics, Philadelphia: SIAM, 1975.
[2] Lighthill, M. J., “Note on the swimming of slender fish”, J. Fluid Mech., (1960), vol. 9, pp.305-317.
[3] Wu, T. Y., “Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins”, J. Fluid Mech., (1971), vol. 46, part 3, pp.545-568.
[4] Blake, R. W., Fish Biomechanics (ed. P. W. Webb & D. Weihs), 1983.
[5] Blake, R. W., Fish Locomotion, Cambridge University Press, 1983.
[6] Ostrowski, J. & Burdick, J., “The geometric mechanics of undulatory robotic locomotion”, International Journal of Robotics Research 17, 7, (1998), pp.683-701.
[7] Ostrowski, J. & Burdick, J., “Gait kinematics for a serpentine robot”, Proceedings — IEEE International Conference on Robotics and Automation 2, (1996), pp.1294-1299.
[8] Cheng, J. Y., Zhuang, L. X. & Tong, B. G., “Analysis of swimming three-dimensional waving plates”, J. Fluid Mech., (1991), vol. 232, pp.341-355.
[9] Azuma, A., The Biokinetics of Flying and Swimming, 1992.
[10] Viedler, J. J. & Hess, F., “Fast continuous swimming of two pelagic predators, Saithe and Mackel: a kinematic analysis”, Journal of Experimental Biology 109, pp.209-228.
[11] Dewar, H., “Studies of tropical tuna swimming performance: thermoregulation, swimming mechanics and energetics”, Ph’d. Thesis in Marine Biology University of California, San Diego (1993).
[12] Barrett, D., Grosenbaugh, M. & Triantafyllou, M., “The optimal control of a flexible hull robotic undersea vehicle propelled by an oscillating foil”, Proceedings of the IEEE Symposium on Autonomous Underwater Vehicle Technology, (1996), pp.1-9.
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