由於日本太空中心(JAXA)發展的太陽風帆「IKAROS」發射成功，美國太空中心(NASA)開始著手進行直升機式(heliogyro)太陽風帆的開發，並於近一兩年提出了明確的設計，將其命名為「HELIOS」。為更有效率地分析此種太陽風帆的薄膜扇葉，莊哲男教授提出了離散質點模型。過去許多研究利用此種方法已經完成了許多分析，包括非耦合的運動分析、偶合兩種運動方式的分析已及強健控制器的設計。本論文改良過去研究的離散質點模型，提出完全耦合運動的離散質點模型。另外，對於由太陽光壓造成的外力項也已完成推導。最重要的是，我們引進彈性模數到離散質點模型當中。本篇論文主要於分析太陽風帆之薄膜扇葉在固定轉數的情況下的穩定性。在系統頻率變化的分析中我們發現顛振(flutter)的現象，此為能夠決定系統穩定性的重要因素。透過累積不同質點數模型的數據，完成對於實際薄膜扇葉不穩定區間的預測。最後，我們利用非線性系統的動態響應來佐證穩定性的分析結果。

In the past few years, NASA proposed and researched a clear design for a heliogyro solar sail called HELIOS (High performance, Enabling, Low-cost, Innovative, Operational Solar sail). A discrete-mass approach has facilitated a large amount of analysis on the spinning membrane blade. In this thesis, we improve the discrete-mass model from that of past research. First, the representation of the motion of the blade has evolved from a system of dual coupling to become fully coupled. Second, the external forcing terms by the solar radiation pressure are derived and applied to the system. Third, the stiffness property is included into the discrete-mass model. Furthermore, this thesis presents an analysis of the stability of the membrane blade under a constant spin rate and varying intensity from solar radiation pressure. The flutter phenomenon, which could be a significant evidence to decide the system's stability, has been demonstrated in the simulation of frequency variation. By collecting results from models consisting of different number of point masses, the convergent conditions for system instability (flutter) have been found. Also, we provide simulations of the non-linear system response to verify the stability results.

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