Superposability of unsteady aerodynamic loads on bridge deck sections

Abstract

The 2-dimensional unsteady aerodynamic forces, in the context of both a thin airfoil where theory of potential flow is always applicable and a bluff bridge-deck section where separated flow is typically induced, are investigated from a point of view of whether or not they conform to the principle of linear superposition in situations of various structural motions and wind gusts. It is shown that some basic preconditions that lead to the linear superposability of the unsteady aerodynamic forces in cases of thin airfoil sections are no longer valid for a bluff section. Theoretical models of bridge aerodynamics such as the one related to flutter-buffeting analysis and those concerning aerodynamic admittance (AA) functions, however, necessitate implicitly this superposability. The contradiction revealed in this work may throw light on the perplexing problem of AA functions pertaining to the description of buffeting loads of bridge decks. Some existing theoretical AA models derived from flutter derivatives according to interrelations valid only for thin airfoil theories, which have been employed rather extensively in bridge aerodynamics, are demonstrated to be illogical. Finally, with full understanding of the preconditions of the applicability of linear superposability of the unsteady aerodynamic forces, suggestions in regard to experiment-based AA functions are presented.

Keywords

bridge unsteady load / aerodynamic load / superposition / buffeting / flutter

References

[1] DowellE HA modern course in aeroelasticity [M], 20044th edsBostonKluwer Academic Publishers95-96

[2] ScanlanR H, TomkoJ J. Airfoil and bridge deck flutter derivatives [J]. Journal of the Engineering Mechanics Division, 1971, 97(EM6): 1717-1737

[3] ScanlanR H, JonesN P. A form of aerodynamic admittance for use in bridge aeroelastic analysis [J]. Fluid Struct, 1999, 13(7/8): 1017-1027

[4] SinghL, JonesN P, ScanlanR H, LorendeauxO. Identification of lateral flutter derivatives of bridge decks [J]. Journal of Wind Engineering and Industrial Aerodynamics, 1996, 60: 81-89

[5] ScanlanR H. Problematics in formulation of wind-force models for bridge decks [J]. Journal of the Engineering Mechanics Division, 1993, 119(7): 1353-1375

[6] HanY, ChenZ Q, HuaX G. New estimation methodology of six complex aerodynamic admittance functions [J]. Wind Struct, 2010, 13(3): 293-307

[7] KarmanT H V, SearsW R. Airfoil theory for non-uniform motion [J]. Aeronaut Sci, 1938, 5(10): 5-15

[8] SearsW R. Some aspects of non-stationary airfoil theory and its practical application [J]. Aeronaut Sci, 1941, 8(3): 104-108

[9] TheodorsenTGeneral theory of aerodynamic instability and the mechanism of flutter [R], 1935LangleyUS Advisory Committee for Aeronautics

[10] ScanlanR H. Motion-related body force functions in two-dimensional low-speed flow [J]. Fluid Struct, 2000, 14(1): 49-63

[11] WagnerH. On the Origin of the dynamic buoyancy of airfoils [J]. Journal of Applied Mathematics and Mechanics, 1925, 5: 17-35

[12] JonesR TThe unsteady lift on a wing of finite aspect ratio [R], 1940LangleyUS Advisory Committee for Aeronautics, Langley

[13] ScanlanR H. Bridge deck aeroelastic admittance revisited [J]. Bridge Eng, 2000, 5(1): 1-7

[14] BorriC, CostaC, ZahltenW. Non-stationary flow forces for the numerical simulation of aeroelastic instability of bridge decks [J]. Comput Struct, 2002, 80(12): 1071-1079

[15] CaracogliaL, JonesN P. Time domain vs. frequency domain characterization of aeroelastic forces for bridge deck sections [J]. Wind Eng Ind Aerodyn, 2003, 91(3): 371-402

[16] LazzariM, VitalianiR V, SaettaA V. Aeroelastic forces and dynamic response of long-span bridges [J]. Int J Numer Method Eng, 2004, 60(6): 1011-1048

[17] CostaC, BorriC. Application of indicial functions in bridge deck aeroelasticity [J]. Wind Eng Ind Aerodyn, 2006, 94(9): 859-881

[18] SalvatoriL, BorriC. Frequency and time-domain methods for the numerical modeling of full-bridge aeroelasticity [J]. Comput Struct, 2007, 85(11/12/13/14): 675-687

[19] ZhangZ T, ChenZ Q, CaiY Y, GeY J. Indicial functions for bridge aero-elastic forces and time-domain flutter analysis [J]. Bridge Eng, 2011, 16(4): 546-557

[20] ChenX, MatsumotoM, KareemA. Time domain flutter and buffeting response analysis of bridges [J]. Eng Mech, 2000, 126(1): 7-16

[21] ChenX, KareemA. Nonlinear response analysis of long-span bridges under turbulent winds [J]. Wind Eng Ind Aerodyn, 2001, 89(14/15): 1335-1350

[22] CaracogliaL. Influence of uncertainty in selected aerodynamic and structural parameters on the buffeting response of long-span bridges [J]. Wind Eng Ind Aerodyn, 2008, 96(3): 327-344

[23] TubinoF. Relationships among aerodynamic admittance functions, flutter derivatives and static coefficients for long-span bridges [J]. Wind Eng Ind Aerodyn, 2005, 93(12): 925-950

[24] GarrickI EOn some reciprocal relations in the theory of nonstationary flows [R], 1938LangleyUS Advisory Committee for Aeronautics, Langley

[25] ScanlanR H. Reexamination of sectional aerodynamic force functions for bridges [J]. Wind Eng Ind Aerodyn, 2001, 89(14/15): 1257-1266

[26] HatanakaA, TanakaH. New estimation method of aerodynamic admittance function [J]. Wind Eng Ind Aerodyn, 2002, 90(12/13/14/15): 2073-2086

[27] HatanakaA, TanakaH. Aerodynamic admittance functions of rectangular cylinders [J]. Wind Eng Ind Aerodyn, 2008, 96(6/7): 945-953

[28] CostaC. Aerodynamic admittance functions and buffeting forces for bridges via indicial functions [J]. Fluid Struct, 2007, 23(3): 413-428

[29] CostaC, BorriC, Olivier FlamandO, GrillaudG. Time-domain buffeting simulations for wind-bridge interaction [J]. Wind Eng Ind Aerodyn, 2007, 95(9/10/11): 991-1006

[30] LaroseG L, TanakaH, GimsingN J, DyrbyeC. Direct measurements of buffeting wind forces on bridge decks [J]. Wind Eng Ind Aerodyn, 1998, 74–76: 809-818

[31] LaroseG L, MannJ. Gust loading on streamlined bridge decks [J]. Fluid Struct, 1998, 12(5): 511-536

[32] DianaG, BruniS, CigadaA, ZappaE. Complex aerodynamic admittance function role in buffeting response of a bridge deck [J]. Wind Eng Ind Aerodyn, 2002, 90(12/13/14/15): 2057-2072

[33] MatsudaM, HikamiY, FujiwaraT, MoriyamaA. Aerodynamic admittance and the ‘strip theory’ for horizontal buffeting forces on a bridge deck [J]. Wind Eng Ind Aerodyn, 1999, 83(1/2/3): 337-346