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

Abstract

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.

Keywords: feather stiffness distribution flexibility matrix optimal Broyden-Fletcher-Goldfarb-Shanno (BFGS)

Received: 16 February 2019
Revised: 08 April 2019
Accepted manuscript online:

PACS:	47.32.cd	(Vortex stability and breakdown)
	47.32.Ff	(Separated flows)

Fund:

Project supported by the National Natural Science Foundation of China (Grant No. 51705459) and the China Postdoctoral Science Foundation.

Corresponding Authors: Di Tang
E-mail: tangdi@zjut.edu.cn

Cite this article:

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 2019 Chin. Phys. B 28 074703

[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
[35]	Liu Z Q, Jiao D, Meyers M A and Zhang Z F 2015 Acta Biomater. 17 137
[2]	Luo He, Hu X X and Wang G Q 2018 Chin. Phys. B 27 028901
[36]	Chao L M, Pan G and Zhang D 2018 Chin. Phys. B 27 114701
[3]	Guo X H, Lin J Z and Nie D M 2009 Chin. Phys. Lett. 26 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
[38]	Weiss I M and Kirchner H O K 2010 J. Exp. Zool. Part A 313A 690
[5]	Wang B and Meyers M A 2017 Acta Biomater. 48 270
[39]	Meleshko V A and Rutman Y L 2017 Procedia Struct. Integrity 6 140
[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
[40]	Tang D, Fan Z Y, Lei M X, Lv B B, Yu L and Cui H 2019 Chin. Phys. B 28 034702
[7]	Spiridon I, Paduraru O M, Rudowski M, Kozlowski M and Darie R N 2012 Ind. Eng. Chem. Res. 51 7279
[41]	Nourmohammadi H and Behjat B 2019 Eng. Anal. Bound. Elem. 99 131
[8]	Daynes S and Weaver P M 2013 Proc. Inst. Mech. Eng. Part D 227 1603
[42]	Wang Q and Yu W B 2017 J. Renewable Sustainable Energy 9 033306
[9]	Hightower B J, Ingersoll R, Chin D D, Lawhon C, Haselsteiner A F and Lentink D 2017 Bioinspir. Biomim. 12 064001
[43]	Guo T Q, Shen E N, Lu Z L and Ding L 2018 Adv. Appl. Math. Mech. 10 1158
[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
[44]	Yuan G L, Wei Z X and Lu X W 2017 Appl. Math. Model 47 811
[11]	Carruthers A C, Thomas A L R, Walker S M and Taylor G K 2010 Aeronaut. J. 114 673
[45]	Deng Y J and Liu Z H 2008 Optim. Methods Softw. 23 395
[12]	Winzen A, Roidl B, Klän S, Klaas M and Schröder W 2014 J. Bionic. Eng. 11 423
[46]	Tang D, Bao S Y, Luo L J, Mao J F, Lv B B and Guo H T 2017 Energy 141 2300
[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
[47]	Yuan G L, Sheng Z, Wang B P, Hu W J and Li C N 2018 J. Comput. Appl. Math. 327 274
[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
[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
[19]	Kowata K, Nakaoka M, Nishio K, Fukao A, Satoh A, Ogoshi M, Takahashi S, Tsudzuki M and Takeuchi S 2014 Gene 542 23
[20]	Lingham-Soliar T 2017 Sci. Rep. 7 45162
[21]	Wang B, Yang W, McKittrick J and Meyers M A 2016 Prog. Mater. Sci. 76 229
[22]	Fraser R D B and David D A P 2011 J. Struct. Biol. 176 340
[23]	McKittrick J, Chen P Y, Bodde S G, Yang W, Novitskaya E E and Meyers M A 2012 JOM 64 449
[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
[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
[28]	Bodde S G, Meyers M A and McKittrick J 2011 J. Mech. Behav. Biomed. Mater. 4 723
[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
[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
[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
[36]	Chao L M, Pan G and Zhang D 2018 Chin. Phys. B 27 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
[39]	Meleshko V A and Rutman Y L 2017 Procedia Struct. Integrity 6 140
[40]	Tang D, Fan Z Y, Lei M X, Lv B B, Yu L and Cui H 2019 Chin. Phys. B 28 034702
[41]	Nourmohammadi H and Behjat B 2019 Eng. Anal. Bound. Elem. 99 131
[42]	Wang Q and Yu W B 2017 J. Renewable Sustainable Energy 9 033306
[43]	Guo T Q, Shen E N, Lu Z L and Ding L 2018 Adv. Appl. Math. Mech. 10 1158
[44]	Yuan G L, Wei Z X and Lu X W 2017 Appl. Math. Model 47 811
[45]	Deng Y J and Liu Z H 2008 Optim. Methods Softw. 23 395
[46]	Tang D, Bao S Y, Luo L J, Mao J F, Lv B B and Guo H T 2017 Energy 141 2300
[47]	Yuan G L, Sheng Z, Wang B P, Hu W J and Li C N 2018 J. Comput. Appl. Math. 327 274

[1]	Nonvanishing optimal noise in cellular automaton model of self-propelled particles Guang-Le Du(杜光乐) and Fang-Fu Ye(叶方富). Chin. Phys. B, 2022, 31(8): 086401.
[2]	Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise Liang'an Huo(霍良安) and Yafang Dong(董雅芳). Chin. Phys. B, 2022, 31(3): 030202.
[3]	Stochastic optimal control for norovirus transmission dynamics by contaminated food and water Anwarud Din and Yongjin Li(黎永锦). Chin. Phys. B, 2022, 31(2): 020202.
[4]	Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Chin. Phys. B, 2022, 31(11): 110204.
[5]	Optimized pulse for stimulated Raman adiabatic passage on noisy experimental platform Zhi-Ling Wang(王志凌), Leiyinan Liu(刘雷轶男), and Jian Cui(崔健). Chin. Phys. B, 2021, 30(8): 080305.
[6]	Leakage of an eagle flight feather and its influence on the aerodynamics Di Tang (唐迪), Dawei Liu(刘大伟), Yin Yang(杨茵), Yang Li(李阳), Xipeng Huang(黄喜鹏), and Kai Liu(刘凯). Chin. Phys. B, 2021, 30(3): 034701.
[7]	Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Chin. Phys. B, 2021, 30(12): 120205.
[8]	CO₂ emission control in new CM car-following model with feedback control of the optimal estimation of velocity difference under V2X environment Guang-Han Peng(彭光含), Rui Tang(汤瑞), Hua Kuang(邝华), Hui-Li Tan(谭惠丽), and Tao Chen(陈陶). Chin. Phys. B, 2021, 30(10): 108901.
[9]	A new car-following model with driver's anticipation effect of traffic interruption probability Guang-Han Peng(彭光含). Chin. Phys. B, 2020, 29(8): 084501.
[10]	Macadam's theory in RGB laser display Guan Wang(王贯), Yuhua Yang(杨雨桦), Tianhao Dong(董天浩), Chun Gu(顾春), Lixin Xu(许立新), Zhongcan Ouyang(欧阳钟灿), Zuyan Xu(许祖彦). Chin. Phys. B, 2019, 28(6): 064209.
[11]	A combined airfoil with secondary feather inspired by the golden eagle and its influences on the aerodynamics Di Tang(唐迪), Zhongyong Fan(范忠勇), Mingxia Lei(雷鸣霞), Binbin Lv(吕彬彬), Li Yu(余立), Hao Cui(崔浩). Chin. Phys. B, 2019, 28(3): 034702.
[12]	Energy-optimal problem of multiple nonholonomic wheeled mobile robots via distributed event-triggered optimization algorithm Ying-Wen Zhang(张潆文), Jin-Huan Wang(王金环), Yong Xu(徐勇), De-Dong Yang(杨德东). Chin. Phys. B, 2019, 28(3): 030501.
[13]	Modeling for heterogeneous multi-stage information propagation networks and maximizing information Ren-Jie Mei(梅人杰), Li Ding(丁李), Xu-Ming An(安栩明), Ping Hu(胡萍). Chin. Phys. B, 2019, 28(2): 028701.
[14]	Optimal estimation of the amplitude of signal with known frequency in the presence of thermal noise Jie Luo(罗杰), Jun Ke(柯俊), Yi-Chuan Liu(柳一川), Xiang-Li Zhang(张祥莉), Wei-Ming Yin(殷蔚明), Cheng-Gang Shao(邵成刚). Chin. Phys. B, 2019, 28(10): 100401.
[15]	Nonlinear suboptimal tracking control of spacecraft approaching a tumbling target Zhan-Peng Xu(许展鹏), Xiao-Qian Chen(陈小前), Yi-Yong Huang(黄奕勇), Yu-Zhu Bai(白玉铸), Wen Yao(姚雯). Chin. Phys. B, 2018, 27(9): 090501.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention