Linear and Nonlinear Aerodynamic Theory of Interaction Between Flexible Long Structure and Wind

XU Xu; CAO Zhi-yuan

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(12): 1299-1308

XU Xu, CAO Zhi-yuan. Linear and Nonlinear Aerodynamic Theory of Interaction Between Flexible Long Structure and Wind[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1299-1308.

Citation:

XU Xu, CAO Zhi-yuan. Linear and Nonlinear Aerodynamic Theory of Interaction Between Flexible Long Structure and Wind[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1299-1308.

Citation:

XU Xu, CAO Zhi-yuan. Linear and Nonlinear Aerodynamic Theory of Interaction Between Flexible Long Structure and Wind[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1299-1308.

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Linear and Nonlinear Aerodynamic Theory of Interaction Between Flexible Long Structure and Wind

XU Xu^1,2,
CAO Zhi-yuan²

1.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
2.
Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, P. R. China

Received Date: 2000-09-06
Rev Recd Date: 2001-07-06
Publish Date: 2001-12-15

Abstract

Abstract

In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed C_i=C_i(β(t),θ),(#em/em#=D,L,M). so, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with "strip theory" and modified "quasi-static theory", and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so called "flutter derivatives" corresponding to the one in the classic equations have been given here, and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the Old Tacoma Bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Bhm's.

Keywords:
nonlinear aerodynamic forces,

coupled interaction,

flutter derivatives

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References(22)

References

[1]
Scanlan R H,Tomko J J.Airfoil and bri dge deck flutter derivatives[J].J Eng Mech,ASCE,1971,97(EM6):17 17-1737.

[2]
Scanlan R H.The action of flexible bridges under wind(Ⅰ) flutte r theory[J].J Sound Vibration,1978,60(2):187-199.

[3]
Lin Y K.Motion of suspension bridges in turbulent winds[J].J Eng Mech,ASCE,1979,105(EM6):921-923.

[4]
Lin Y K,Ariaratnam S T.Stability of bridge motionin turbulent winds[J].J Struct Mech,1980,8(1):1-15.

[5]
Scanlan R H.The action of flexible bridge under wind(Ⅱ) buffeti ng theory[J].J Sound Vibration,1978,60(2):201-211.

[6]
Davenport A G.The response of slender,line-like structures to a gusty wind[J].Proceedings ICE,1962,23:389-407.

[7]
Scanlan R H.Interpreting aeroelastic models of cable-stay ed bridg es[J].J Eng Mech,ASCE,1987,113(4):555-575.

[8]
Sarkar P P,et al.Identification of aeroelastic parameters of fle xible bridges[J].J Eng Mech,ASCE,1994,120(8):1718-1742.

[9]
Piccardo G.A methodology for the study of coupled aeroelastic phenomena[J].J Wind Eng Indus Aerodynamic,1993,48:241-252.

[10]
Solari G.Gust-Excited Vibrations[M].New York:Springer-Ve rlag,1994.

[11]
Strïmmen E,Hiorth-Hansen E.The buffeting wind loading of structural members at an arbitrary attitude in the flow[J].J Wind Eng Indus Aerod ynamic,1995,56:267-290.

[12]
Brito J L V,Riera J D.Aerodynamic instability of cylindrical bluff bodies in non-homogeneous flow[J].J Wind Eng Indus Aerodynamic,1995,57,81-96.

[13]
Parkinson G V,Brooks N P H.On the aeroelastic instability of bluff cylinders[J].J Appl Mech,1961,83:250-258.

[14]
Novak M.Aeroelastic galloping of rigid and elastic bodies[R].Univ Western Ontorio,London/Canada,Res Rep BLWT-3-68,1968.

[15]
Bhm V F.Berechnugn nichtlinearer aerodynamisch erregter schwin gungen von Hangebrucken[J].Der Stahlbau,1967,7:207-215.

[16]
Falco M,Curami A,Zasso A.Nonlinear effects in sectional model aeroelastic parameters[J].J Wind Eng Indus Aerodynamic,1992,41-44:1321-1332.

[17]
Diana G,Cheli F,Resta F.Time domain aeroelastic force identification on bridge decks[A].In:9th International Conference of Wind Engineering[C].New Delhi,India,1995,938-949.

[18]
Borri C,Hffer R,Zahlten W.A nonlinear approach for evaluating simultaneous buffeting and aeroelastic effects on bridge decks[A].In:9 the International Conference of Wind Engineering[C].New Delhi,India,1995,839-850.

[19]
Steinmann D G,Hangebrücken-Das aerodynamische problem und seine lsung[J].Acier-Steel-Stahl,1954,19(10-11):495,542.

[20]
Scanlan R H,Jones N P,Singh L.Inter-relation among flutter derivatives[J].J Wind Eng Indus Aerodynamic,1997,69-71:829-837.

[21]
XU Xu,CAO Zhi-yuan.New expressions of nonlinear aerodynamic for ces in civil engineering[A].In:Proceedings of the 3rd Int Conf on Nonlinear Mech(ICNM-Ⅲ)[C].Shanghai:Shanghai University Press,Aug,1998,396-401.

[22]
徐旭,曹志远.气动耦合扭转非线性振动的稳定性分析[J].非线性动力学学报,1999,6(3):228-234.

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[1]	Scanlan R H,Tomko J J.Airfoil and bri dge deck flutter derivatives[J].J Eng Mech,ASCE,1971,97(EM6):17 17-1737.
[2]	Scanlan R H.The action of flexible bridges under wind(Ⅰ) flutte r theory[J].J Sound Vibration,1978,60(2):187-199.
[3]	Lin Y K.Motion of suspension bridges in turbulent winds[J].J Eng Mech,ASCE,1979,105(EM6):921-923.
[4]	Lin Y K,Ariaratnam S T.Stability of bridge motionin turbulent winds[J].J Struct Mech,1980,8(1):1-15.
[5]	Scanlan R H.The action of flexible bridge under wind(Ⅱ) buffeti ng theory[J].J Sound Vibration,1978,60(2):201-211.
[6]	Davenport A G.The response of slender,line-like structures to a gusty wind[J].Proceedings ICE,1962,23:389-407.
[7]	Scanlan R H.Interpreting aeroelastic models of cable-stay ed bridg es[J].J Eng Mech,ASCE,1987,113(4):555-575.
[8]	Sarkar P P,et al.Identification of aeroelastic parameters of fle xible bridges[J].J Eng Mech,ASCE,1994,120(8):1718-1742.
[9]	Piccardo G.A methodology for the study of coupled aeroelastic phenomena[J].J Wind Eng Indus Aerodynamic,1993,48:241-252.
[10]	Solari G.Gust-Excited Vibrations[M].New York:Springer-Ve rlag,1994.
[11]	Strïmmen E,Hiorth-Hansen E.The buffeting wind loading of structural members at an arbitrary attitude in the flow[J].J Wind Eng Indus Aerod ynamic,1995,56:267-290.
[12]	Brito J L V,Riera J D.Aerodynamic instability of cylindrical bluff bodies in non-homogeneous flow[J].J Wind Eng Indus Aerodynamic,1995,57,81-96.
[13]	Parkinson G V,Brooks N P H.On the aeroelastic instability of bluff cylinders[J].J Appl Mech,1961,83:250-258.
[14]	Novak M.Aeroelastic galloping of rigid and elastic bodies[R].Univ Western Ontorio,London/Canada,Res Rep BLWT-3-68,1968.
[15]	Bhm V F.Berechnugn nichtlinearer aerodynamisch erregter schwin gungen von Hangebrucken[J].Der Stahlbau,1967,7:207-215.
[16]	Falco M,Curami A,Zasso A.Nonlinear effects in sectional model aeroelastic parameters[J].J Wind Eng Indus Aerodynamic,1992,41-44:1321-1332.
[17]	Diana G,Cheli F,Resta F.Time domain aeroelastic force identification on bridge decks[A].In:9th International Conference of Wind Engineering[C].New Delhi,India,1995,938-949.
[18]	Borri C,Hffer R,Zahlten W.A nonlinear approach for evaluating simultaneous buffeting and aeroelastic effects on bridge decks[A].In:9 the International Conference of Wind Engineering[C].New Delhi,India,1995,839-850.
[19]	Steinmann D G,Hangebrücken-Das aerodynamische problem und seine lsung[J].Acier-Steel-Stahl,1954,19(10-11):495,542.
[20]	Scanlan R H,Jones N P,Singh L.Inter-relation among flutter derivatives[J].J Wind Eng Indus Aerodynamic,1997,69-71:829-837.
[21]	XU Xu,CAO Zhi-yuan.New expressions of nonlinear aerodynamic for ces in civil engineering[A].In:Proceedings of the 3rd Int Conf on Nonlinear Mech(ICNM-Ⅲ)[C].Shanghai:Shanghai University Press,Aug,1998,396-401.
[22]	徐旭,曹志远.气动耦合扭转非线性振动的稳定性分析[J].非线性动力学学报,1999,6(3):228-234.

Linear and Nonlinear Aerodynamic Theory of Interaction Between Flexible Long Structure and Wind

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