本研究將根據由中科院於低速風洞吹試條件下，設計之複材機翼模型為基礎，以等向性材料等效出可以近似複材機翼模型自由振動模態和顫振現象的等效機翼模型。主要分成四個部分，包含數值模擬模態分析、地面振動測試、顫振數值分析和風洞吹試。首先，複材機翼由玻璃纖維蒙皮和C形前樑以及高密度發泡材填充而成，將複材機翼模型放入數值模擬軟體進行模態分析，得出等效機翼模型的目標模態振型以及自然頻率，接著透過複材機翼模型截面上的各方向質量慣性矩作為等效樑截面的設計條件，在考量挫曲強度之後，選用長19 mm、高12 mm、腹板厚度2 mm和翼緣板厚度3 mm作為最終截面設計，並且將腹板前端840 mm的腹板上距離中心線0.5mm上下錯開，挖直徑4 mm的孔洞共166個孔。將上述複材機翼模型以及等效樑送往屏東科技大學振動噪音實驗室進行地面振動測試，進行自由邊界和固定末端兩個孔這兩種邊界條件，並以地面振動結果修正數值模擬模態建模，複材機翼模型的部分，主要修正中心高密度發泡材的結構材料參數，等效樑則是修正邊界條件上的誤差。接著針對等效機翼模型配重，使用3D列印PETG翼肋，並且翼前緣插上14 g的鉛條，將重心配在等效樑上，假設蒙皮不提供結構勁度的理想條件，此種配重的等效機翼模型可以得到和複材機翼模型，誤差4%以內的模態頻率，然而使用PETG進行蒙皮會提供結構平擺模態勁度，導致誤差提高。最後將等效機翼模型和複材機翼模型以相同的氣動力網格和全域氣動力參數建模，以此獲得顫振風速和頻率。由於顫振模態為平擺模態，受到等效機翼模型本身結構阻尼大於複材機翼模型的影響，加上蒙皮提供平擺模態額外勁度，導致等效機翼模型顫振風速比複材機翼模型高12.225 m/s，顫振頻率上也提高4.058 Hz。最後進行等效機翼模型的風洞吹試實驗，分別將加速規黏貼於I型前樑頂端和翼肋中段收取振動訊號，並且和顫振數值分析結果進行比較，經過特徵頻率的比較分析之後，可以確認數值分析的結過具有一定的可靠性，然而實際模型的3D列印翼肋並非理想剛體，導致振動過程中，翼肋和I型前樑的緊配孔會發生形變，造成實體等效機翼模型沒有在顫振數值模擬得到的顫振風速發生顫振。

In this research, a similarity model of composite wing model with isotropic material was developed, which was verified by ground vibration testing (GVT) and wind tunnel testing. First, building a numerical model based on the composite wing model designed by National Chung-Shan Institute of Science & Technology (NCSIST) for low-speed wind tunnel. The Modal shape and the modal frequency could be calculated by setting the material parameters of each part of the composite wing model and the boundary conditions for the numerical model. To design the similarity beam section, the moment of inertia of the composite wing section was determined as the design parameter. Considering the design parameters and buckling stiffness, the section of the similarity beam was designed as I-shape with 19 mm length, 12 mm height, 2 mm web and 3 mm flange. Moreover, the similarity beam was totally dug 166 holes with 4 mm diameter on the web to decrease the torsion stiffness. After manufacturing the composite wing model and the similarity beam, it was going to do the GVT. As a result of the GVT tests, the numerical model of the composite wing and similarity beam could be verified as being realistic. Furthermore, the final similarity wing model was obtained by the similarity beam with 3D-printed ribs and skin with 14 g lead beams as counterweight. Setting up the aerodynamic configuration, the flutter speed and flutter frequency can be calculated by the numerical analysis.
Assuming the skin didn’t provide any structural stiffness, the error of the modal frequency of the similarity wing model compared with the composite model is lower than 4%. However, the skin of the realistic similarity wing model provided extra structural stiffness, and the error of the modal frequencies increased. Since the structural stiffness of the similarity beam was higher than that of the composite wing model, the similarity wing model had a higher flutter speed of 12.225 m/s and a higher flutter frequency of 4.058 Hz than those of the composite wing model. Moreover, since the 3D-printed ribs were not rigid bodies, the wind tunnel testing of the realistic similarity wing model didn’t flutter as the flutter speed of the numerical result achieved. The further research could improve the similarity of the modal and flutter results of the similarity wing model by choosing other design parameters and materials of the design process.

[1] C. B. Hwu and M. C. Yu, "A Comprehensive Finite Element Model for Tapered Composite Wing Structures," Cmes-Comp Model Eng, vol. 67, no. 2, pp. 151-173, 2010.
[2] 吳誌賢, "空氣彈力系統動態分析與顫振控制," 碩士論文, 航空太空工程學系, 國立成功大學, 2010.
[3] K. Menon and R. Mittal, "Computational Modelling and Analysis of Aeroelastic Flutter," in 2018 Fluid Dynamics Conference, pp. 3080, 2018.
[4] Q. Yan and Z. Wan, "A Highly Efficient Aeroelastic Analysis Method Based on External Aerodynamic Force and Strip Theory," in 2018 AIAA Aerospace Sciences Meeting, pp. 2068, 2018.
[5] N. Tsushima and W. H. Su, "Flutter Suppression for Highly Flexible Wings Using Passive and Active Piezoelectric Effects," Aerosp Sci Technol, vol. 65, pp. 78-89, 2017.
[6] Simitses GJ, Rezaeepazhand J., "Structural Similitude and Scaling Laws for Laminated Beam Plates," National Aeronautics and Space Administration, Technical Report NASA CR-190585, 1922.
[7] Jha A. Dynamic, "Testing of Structures Using Scale Models," In 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, pp. 2259, 2005.
[8] Harris HG, "Sabnis GM. Structural Modeling and Experimental Techniques," CRC press, 1999.
[9] Young DF., "Basic Principles and Concepts of Model Analysis," Exp Mech, 11:pp. 325–36, 1971.
[10] Chambers JR., "Modeling Fight: the Role of Dynamically Scaled Free Fight Models in Support of NASA’s Aerospace Programs," National Aeronautics and Space Administration, Technical Report NASA SP-2009-575, 2009.
[11] Szucs E., "Similitude and Modeling," New York: Elsevier, 1980.
[12] Ramu M, Prabhu Raja V, Thyla PR., "Establishment of Structural Similitude for Elastic Models and Validation of Scaling Laws," KSCE J Civil Eng,17:pp. 139–44, 2013.
[13] Wissmann JW, "Dynamic Stability of Space Vehicles Structural Dynamics Model Testing," National Aeronautics and Space Administration, Technical Report NASA CR-1195, 1968.
[14] Jaszlics IJ, Park AC., "Use of Dynamic Scale Models to Determine Launch Vehicle Characteristics – Volume 1: Analytical Investigation," National Aeronautics and Space Administration, Technical Report NASA CR-102272, 1969.
[15] Penning FA., "Use of Dynamic Scale Models to Determine Launch Vehicle Characteristics – Volume II: Experimental Investigation," National Aeronautics and Space Administration, Technical Report NASA CR-102280, 1969.
[16] Wolowicz CH, Bowman James SJ, Gilbert WP., "Similitude Requirements and Scaling Relationships as Applied to Model Testing," National Aeronautics and Space Administration, Technical Report NASA TP-1435, 1979.
[17] Williams M, Blakeborough A., "Laboratory Testing of Structures Under Dynamic Loads: An Introductory Review," Philos Trans Roy Soc Lond A: Math Phys Eng Sci, 359:1651–69,2001
[18] Kumar S, Itoh Y, Saizuka K, Usami T., "Pseudodynamic Testing of Scaled Models," J Struct Eng, 123:524–6, 1997.
[19] Kim NS, Kwak YH, Chang SP, "Pseudodynamic Tests on Small Scale Steel Models," In: 13th World conference on earthquake engineering, Vancouver, B. C., Canada.
[20] V. C. Sherrer, T. J. Hertz, and M. H. Shirk, "Wind Tunnel Demonstration of Aeroelastic Tailoring Applied to Forward Swept Wings," Journal of Aircraft 18.11, pp. 976-983, 1981.
[21] J. Rezaeepazhand, and Ali A. Yazdi, "Similitude Requirements and Scaling Laws For Flutter Prediction of Angle-Ply Composite Plates," Composites Part B: Engineering 42.1, pp. 51-56, 2011.
[22] Ali A. Yazdi, and J. Rezaeepazhand, "Accuracy of Scale Models for Flutter Prediction of Cross-Ply Laminated Plates," Journal of Reinforced Plastics and Composites 30.1, pp. 45-52, 2011.
[23] Zeng, Jie, et al., "Ground vibration test identified structure model for flutter envelope prediction," In AIAA Atmospheric Flight Mechanics Conference, pp. 4856, 2012.
[24] C. You, M. Yasaee, and I. Dayyani, "Structural Similitude Design for a Scaled Composite Wing Box Based on Optimised Stacking Sequence," Composite Structures 226 : 111255, 2019.
[25] C. Black, K. V. Singh, S. Goodman, A. Altman, and R. M. Kolonay, "Design, fabrication and testing of 3D printed wings for rapid evaluation of aeroelastic performance," in 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, pp. 1997, 2018.
[26] A. M. Pankonien and G. W. Reich, "Multi-Material Printed Wind-Tunnel Flutter Model," Aiaa Journal, vol. 56, no. 2, pp. 793-807, 2018, doi: 10.2514/1.J056097.
[27] M. Karpel, "Design for Active and Passive Flutter Suppression and Gust Alleviation," NASA, Contractor Report 3482, 1981.
[28] E. Verstraelen, G. Habib, G. Kerschen, and G. Dimitriadis, "Experimental Passive Flutter Suppression Using a Linear Tuned Vibration Absorber," Aiaa Journal, vol. 55, no. 5, pp. 1707-1722, 2017.
[29] V. A. J. Butoescu, "Similitude Criteria for Aeroelastic Models," INCAS Bulletin, vol. 7, no. 1, pp. 37, 2015.
[30] Y. C. Fung, An introduction to the theory of aeroelasticity. Courier Dover Publications, 2008.