Measuring the flexibility matrix of an eagle's flight feather and a method to estimate the stiffness distribution

doi:10.1088/1674-1056/28/7/074703

中国物理B ›› 2019, Vol. 28 ›› Issue (7): 74703-074703.doi: 10.1088/1674-1056/28/7/074703

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Measuring the flexibility matrix of an eagle's flight feather and a method to estimate the stiffness distribution

Di Tang(唐迪), Hai Zhu(朱海), Wei Yuan(袁巍), Zhongyong Fan(范忠勇), Mingxia Lei(雷鸣霞)

1 College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China;
2 High Speed Aerodynamic Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China;
3 Zhejiang Museum of Natural History, Hangzhou 310014, China

收稿日期:2019-02-16 修回日期:2019-04-08 出版日期:2019-07-05 发布日期:2019-07-05
通讯作者: Di Tang E-mail:tangdi@zjut.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 51705459) and the China Postdoctoral Science Foundation.

Measuring the flexibility matrix of an eagle's flight feather and a method to estimate the stiffness distribution

Di Tang(唐迪)^1,2, Hai Zhu(朱海)¹, Wei Yuan(袁巍)¹, Zhongyong Fan(范忠勇)³, Mingxia Lei(雷鸣霞)³

1 College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China;
2 High Speed Aerodynamic Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China;
3 Zhejiang Museum of Natural History, Hangzhou 310014, China

Received:2019-02-16 Revised:2019-04-08 Online:2019-07-05 Published:2019-07-05
Contact: Di Tang E-mail:tangdi@zjut.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 51705459) and the China Postdoctoral Science Foundation.

摘要/Abstract

摘要：

Flight feathers stand out with extraordinary mechanical properties for flight because they are lightweight but stiff enough. Their elasticity has great effects on the aerodynamics, resulting in aeroelasticity. Our primary task is to figure out the stiffness distribution of the feather to study the aeroelastic effects. The feather shaft is simplified as a beam, and the flexibility matrix of an eagle flight feather is tested. A numerical method is proposed to estimate the stiffness distributions along the shaft length based on an optimal Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with global convergence. An analysis of the compressive behavior of the shaft based on the beam model shows a good fit with experimental results. The stiffness distribution of the shaft is finally presented using a 5th order polynomial.

关键词: feather, stiffness distribution, flexibility matrix, optimal, Broyden-Fletcher-Goldfarb-Shanno (BFGS)

Abstract:

Key words: feather, stiffness distribution, flexibility matrix, optimal, Broyden-Fletcher-Goldfarb-Shanno (BFGS)

中图分类号: (Vortex stability and breakdown)

47.32.cd

47.32.Ff (Separated flows)

唐迪, 朱海, 袁巍, 范忠勇, 雷鸣霞. Measuring the flexibility matrix of an eagle's flight feather and a method to estimate the stiffness distribution[J]. 中国物理B, 2019, 28(7): 74703-074703.

Di Tang(唐迪), Hai Zhu(朱海), Wei Yuan(袁巍), Zhongyong Fan(范忠勇), Mingxia Lei(雷鸣霞). Measuring the flexibility matrix of an eagle's flight feather and a method to estimate the stiffness distribution[J]. Chin. Phys. B, 2019, 28(7): 74703-074703.

参考文献 47

[34]	Corning W R and Biewener A A 1998 J. Exp. Biol. 201 3057
[1]	Sullivan T N, Wang B, Espinosa H D and Meyers M A 2017 Mater. Today 20 377 doi: 10.1016/j.mattod.2017.02.004
[35]	Liu Z Q, Jiao D, Meyers M A and Zhang Z F 2015 Acta Biomater. 17 137 doi: 10.1016/j.actbio.2015.01.035
[2]	Luo He, Hu X X and Wang G Q 2018 Chin. Phys. B 27 028901 doi: 10.1088/1674-1056/27/2/028901
[36]	Chao L M, Pan G and Zhang D 2018 Chin. Phys. B 27 114701 doi: 10.1088/1674-1056/27/11/114701
[3]	Guo X H, Lin J Z and Nie D M 2009 Chin. Phys. Lett. 26 084701 doi: 10.1088/0256-307X/26/8/084701
[37]	Crenshaw D G 1980 J. Biomech. 13 199
[4]	Altshuler D L, Bahlman J W, Dakin R, Gaede A H, Goller B, Lentink D, Segre P S and Skandalisa D A 2015 Can. J. Zool. 93 961 doi: 10.1139/cjz-2015-0103
[38]	Weiss I M and Kirchner H O K 2010 J. Exp. Zool. Part A 313A 690 doi: 10.1002/jez.641
[5]	Wang B and Meyers M A 2017 Acta Biomater. 48 270 doi: 10.1016/j.actbio.2016.11.006
[39]	Meleshko V A and Rutman Y L 2017 Procedia Struct. Integrity 6 140 doi: 10.1016/j.prostr.2017.11.022
[6]	Tang D, Bao S Y, Xu M, Luo L J, Lv B B, Yu L and Cui H 2019 Ann. Nucl. Energy 124 198 doi: 10.1016/j.anucene.2018.10.008
[40]	Tang D, Fan Z Y, Lei M X, Lv B B, Yu L and Cui H 2019 Chin. Phys. B 28 034702 doi: 10.1088/1674-1056/28/3/034702
[7]	Spiridon I, Paduraru O M, Rudowski M, Kozlowski M and Darie R N 2012 Ind. Eng. Chem. Res. 51 7279 doi: 10.1021/ie300738d
[41]	Nourmohammadi H and Behjat B 2019 Eng. Anal. Bound. Elem. 99 131 doi: 10.1016/j.enganabound.2018.11.006
[8]	Daynes S and Weaver P M 2013 Proc. Inst. Mech. Eng. Part D 227 1603 doi: 10.1177/0954407013496557
[42]	Wang Q and Yu W B 2017 J. Renewable Sustainable Energy 9 033306 doi: 10.1063/1.4985091
[9]	Hightower B J, Ingersoll R, Chin D D, Lawhon C, Haselsteiner A F and Lentink D 2017 Bioinspir. Biomim. 12 064001 doi: 10.1088/1748-3190/aa7eb2
[43]	Guo T Q, Shen E N, Lu Z L and Ding L 2018 Adv. Appl. Math. Mech. 10 1158 doi: 10.4208/aamm.OA-2017-0342
[10]	Chen K, Liu Q P, Liao G H, Yang Y, Ren L Q, Yang H X and Chen X 2012 J. Bionic. Eng. 9 192 doi: 10.1016/S1672-6529(11)60109-1
[44]	Yuan G L, Wei Z X and Lu X W 2017 Appl. Math. Model 47 811 doi: 10.1016/j.apm.2017.02.008
[11]	Carruthers A C, Thomas A L R, Walker S M and Taylor G K 2010 Aeronaut. J. 114 673 doi: 10.1017/S0001924000004152
[45]	Deng Y J and Liu Z H 2008 Optim. Methods Softw. 23 395 doi: 10.1080/10556780701669370
[12]	Winzen A, Roidl B, Klän S, Klaas M and Schröder W 2014 J. Bionic. Eng. 11 423 doi: 10.1016/S1672-6529(14)60055-X
[46]	Tang D, Bao S Y, Luo L J, Mao J F, Lv B B and Guo H T 2017 Energy 141 2300 doi: 10.1016/j.energy.2017.11.105
[13]	Moller A P and Swaddle J P 1998 Asymmetry, Developmental Stability, and Evolution (Oxford: Oxford University Press)
[14]	Ákos Z, Nagy M and Vicsek T 2008 Proc. Natl. Acad. Sci. USA 105 4139 doi: 10.1073/pnas.0707711105
[47]	Yuan G L, Sheng Z, Wang B P, Hu W J and Li C N 2018 J. Comput. Appl. Math. 327 274 doi: 10.1016/j.cam.2017.05.030
[15]	Altenbuchner C and Hubbard J E Jr. 2018 Modern Flexible Multi-Body Dynamics Modeling Methodology for Flapping Wing Vehicles (London: Academic Press) pp. 109-127
[16]	Choudary R B, Krishna N N and Bhargava N R M R 2018 Mater. Today: Proc. 5 8514 doi: 10.1016/j.matpr.2017.11.548
[17]	Astbury W T and Marwick T C 1932 Nature 130 309
[18]	Fraser R D B and Parry D A D 2011 J. Struct. Biol. 173 391 doi: 10.1016/j.jsb.2010.09.020
[19]	Kowata K, Nakaoka M, Nishio K, Fukao A, Satoh A, Ogoshi M, Takahashi S, Tsudzuki M and Takeuchi S 2014 Gene 542 23 doi: 10.1016/j.gene.2014.03.027
[20]	Lingham-Soliar T 2017 Sci. Rep. 7 45162 doi: 10.1038/srep45162
[21]	Wang B, Yang W, McKittrick J and Meyers M A 2016 Prog. Mater. Sci. 76 229 doi: 10.1016/j.pmatsci.2015.06.001
[22]	Fraser R D B and David D A P 2011 J. Struct. Biol. 176 340 doi: 10.1016/j.jsb.2011.08.010
[23]	McKittrick J, Chen P Y, Bodde S G, Yang W, Novitskaya E E and Meyers M A 2012 JOM 64 449 doi: 10.1007/s11837-012-0302-8
[24]	Lingham-Soliar T and Murugan N 2013 PLoS One 8 e65849
[25]	Finlay K A, Gawryla M D and Schiraldi D A 2015 Materials 8 5440 doi: 10.3390/ma8085258
[26]	Filshie B K and Rogers G E 1962 J. Cell Biol. 13 1
[27]	Earland C, Blakey P R and Stell J G P 1962 Nature 196 1287 doi: 10.1038/1961287a0
[28]	Bodde S G, Meyers M A and McKittrick J 2011 J. Mech. Behav. Biomed. Mater. 4 723 doi: 10.1016/j.jmbbm.2011.01.010
[29]	Laurent C M, Palmer C, Boardman R P, Dyke G and Cook R B 2013 J. R. Soc. Interface 8 e65849
[30]	Özmen U and Baba B O 2016 Mater. Tehnol. 50 141 doi: 10.17222/mit.2014.182
[31]	Bonser R H C and Purslow P P 1995 J. Exp. Biol. 198 1029
[32]	Weiss I M and Kirchner H O K 2010 J. Exp. Zool. Part A 313 690
[33]	Bachmann T, Emmerlich J, Baumgartner W, Schneider J M and Wagner H 2012 J. Exp. Biol. 215 405 doi: 10.1242/jeb.059451
[34]	Corning W R and Biewener A A 1998 J. Exp. Biol. 201 3057
[35]	Liu Z Q, Jiao D, Meyers M A and Zhang Z F 2015 Acta Biomater. 17 137 doi: 10.1016/j.actbio.2015.01.035
[36]	Chao L M, Pan G and Zhang D 2018 Chin. Phys. B 27 114701 doi: 10.1088/1674-1056/27/11/114701
[37]	Crenshaw D G 1980 J. Biomech. 13 199
[38]	Weiss I M and Kirchner H O K 2010 J. Exp. Zool. Part A 313A 690 doi: 10.1002/jez.641
[39]	Meleshko V A and Rutman Y L 2017 Procedia Struct. Integrity 6 140 doi: 10.1016/j.prostr.2017.11.022
[40]	Tang D, Fan Z Y, Lei M X, Lv B B, Yu L and Cui H 2019 Chin. Phys. B 28 034702 doi: 10.1088/1674-1056/28/3/034702
[41]	Nourmohammadi H and Behjat B 2019 Eng. Anal. Bound. Elem. 99 131 doi: 10.1016/j.enganabound.2018.11.006
[42]	Wang Q and Yu W B 2017 J. Renewable Sustainable Energy 9 033306 doi: 10.1063/1.4985091
[43]	Guo T Q, Shen E N, Lu Z L and Ding L 2018 Adv. Appl. Math. Mech. 10 1158 doi: 10.4208/aamm.OA-2017-0342
[44]	Yuan G L, Wei Z X and Lu X W 2017 Appl. Math. Model 47 811 doi: 10.1016/j.apm.2017.02.008
[45]	Deng Y J and Liu Z H 2008 Optim. Methods Softw. 23 395 doi: 10.1080/10556780701669370
[46]	Tang D, Bao S Y, Luo L J, Mao J F, Lv B B and Guo H T 2017 Energy 141 2300 doi: 10.1016/j.energy.2017.11.105
[47]	Yuan G L, Sheng Z, Wang B P, Hu W J and Li C N 2018 J. Comput. Appl. Math. 327 274 doi: 10.1016/j.cam.2017.05.030

Measuring the flexibility matrix of an eagle's flight feather and a method to estimate the stiffness distribution

Measuring the flexibility matrix of an eagle's flight feather and a method to estimate the stiffness distribution

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