Methods for flutter stability analysis of long-span bridges: a review

Predicting the phenomenon of aerodynamic instability is essential for the analysis and design of long-span cable-supported bridges. This paper reviews the history and development of aerodynamic analysis techniques and state-of-the-art numerical and experimental methods for flutter stability analysis. A discussion of the flutter phenomenon is followed by a literature review. This study provides a perspective on self-excited aerodynamic force models, identification of aerodynamic derivatives and methods for determining aerodynamic instability of long-span bridges in two dimensions and three dimensions. Computational fluid dynamics (CFD) techniques for modelling the flow past bluff bodies are also covered. Different model combination techniques are presented, utilising analytical, numerical and experimental approaches to predict the flutter limit. The effect of different parameters on the flutter stability limit is also highlighted. Furthermore, an overview of the complementary relationship between wind tunn...

[1]  R. Scanlan,et al.  Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks , 1991 .

[2]  W. M. Adams,et al.  Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces , 1988 .

[3]  Palle Thoft-Christensen,et al.  Suspension Bridge Flutter for Girders with Separate Control Flaps , 2001 .

[4]  Earl H. Dowell,et al.  Flutter and limit cycle oscillations of two-dimensional panels in three-dimensional axial flow , 2003 .

[5]  Jin Cheng,et al.  Aerostatic stability analysis of suspension bridges under parametric uncertainty , 2003 .

[6]  Kiran Singh,et al.  The effect of non-uniform damping on flutter in axial flow and energy-harvesting strategies , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Ahsan Kareem,et al.  Aeroelastic Analysis of Bridges under Multicorrelated Winds: Integrated State-Space Approach , 2001 .

[8]  Nicholas P. Jones,et al.  Multimode coupled flutter and buffeting analysis of the Akashi-Kaikyo bridge , 1999 .

[9]  Robert H. Scanlan,et al.  The action of flexible bridges under wind, II: Buffeting theory , 1978 .

[10]  Virote Boonyapinyo,et al.  Data-driven stochastic subspace identification of flutter derivatives of bridge decks , 2010 .

[11]  F. Nieto,et al.  Bridge deck flutter derivatives: Efficient numerical evaluation exploiting their interdependence , 2015 .

[12]  Ramana V. Grandhi,et al.  Quantification of Modeling Uncertainty in Aeroelastic Design , 2010 .

[13]  Theodore Theodorsen,et al.  Mechanism of flutter: A theoretical and experimental investigation of the flutter problem , 1938 .

[14]  Y. J. Ge,et al.  Aerodynamic Stability of Long-Span Suspension Bridges under Erection , 2000 .

[15]  Pedro Albrecht,et al.  Flutter derivatives based random parametric excitation aerodynamic analysis , 2000 .

[16]  Ld D. Zhu,et al.  Tsing Ma bridge deck under skew winds—Part II: flutter derivatives , 2002 .

[17]  Ahsan Kareem,et al.  Efficacy of Tuned Mass Dampers for Bridge Flutter Control , 2003 .

[18]  Hiroshi Tanaka,et al.  Modelling uncertainties in prediction of aeroelastic bridge behaviour , 2003 .

[19]  Guido Morgenthal,et al.  A comparative study of numerical methods for fluid structure interaction analysis in long-span bridge design , 2002 .

[20]  T. Theodorsen General Theory of Aerodynamic Instability and the Mechanism of Flutter , 1934 .

[21]  Rui Zhou,et al.  Aerodynamic instability performance of twin box girders for long-span bridges , 2015 .

[22]  Ahsan Kareem,et al.  EFFICACY OF THE IMPLIED APPROXIMATION IN THE IDENTIFICATION OF FLUTTER DERIVATIVES , 2004 .

[23]  Santiago Hernández,et al.  Analytical approach to sensitivity analysis of flutter speed in bridges considering variable deck mass , 2011, Adv. Eng. Softw..

[24]  J. Sørensen,et al.  Discrete Vortex Method for Two-dimensional Flow past Bodies of Arbitrary Shape Undergoing Prescribed Rotary and Translational Motion , 1994 .

[25]  Y. Nakamura,et al.  On the aerodynamic mechanism of torsional flutter of bluff structures , 1979 .

[26]  Akhil Upadhyay,et al.  Support vector machine based aerodynamic analysis of cable stayed bridges , 2009, Adv. Eng. Softw..

[27]  Prem Krishna,et al.  Relevance of Eighteen Flutter Derivatives in Wind Response of a Long-Span Cable-Stayed Bridge , 2008 .

[28]  Ahsan Kareem,et al.  Simulation of nonlinear bridge aerodynamics: A sparse third-order Volterra model , 2014 .

[29]  Gianni Bartoli,et al.  A simplified approach to bridge deck flutter , 2008 .

[30]  Haifan Xiang,et al.  Nonlinear aerostatic and aerodynamic analysis of long-span suspension bridges considering wind-structure interactions , 2002 .

[31]  Yaojun Ge,et al.  Recent development of bridge aerodynamics in China , 2008 .

[32]  Andrea Collina,et al.  Turbulence effect on flutter velocity in long span suspended bridges , 1993 .

[33]  Luca Caracoglia,et al.  Influence of uncertainty in selected aerodynamic and structural parameters on the buffeting response of long-span bridges , 2008 .

[34]  Pier Marzocca,et al.  Indicial functions in the aeroelasticity of bridge decks , 2014 .

[35]  Omar M. Knio,et al.  Estimation of the flutter derivatives of an NACA airfoil by means of Navier–Stokes simulation , 2003 .

[36]  Hitoshi Yamada,et al.  Flutter responses in long span bridges with wind induced displacement by the mode tracing method , 1998 .

[37]  Wai-Fah Chen,et al.  Bridge Engineering Handbook , 1999 .

[38]  Sungmoon Jung,et al.  Effect of uncertainties in wind speed and direction on the fatigue damage of long-span bridges , 2015 .

[39]  X. G. Hua,et al.  Full-order and multimode flutter analysis using ANSYS , 2008 .

[40]  Bin Wang,et al.  Numerical simulation for aerodynamic derivatives of bridge deck , 2009, Simul. Model. Pract. Theory.

[41]  Masaru Matsumoto,et al.  Flutter instability and recent development in stabilization of structures , 2007 .

[42]  Ahsan Kareem,et al.  A nonlinear convolution scheme to simulate bridge aerodynamics , 2013 .

[43]  Ahsan Kareem,et al.  Revisiting Multimode Coupled Bridge Flutter: Some New Insights , 2006 .

[44]  Kazushi Ogawa,et al.  AERODYNAMIC CHARACTERISTICS OF 2-BOX GIRDER SECTION ADAPTABLE FOR SUPER-LONG SPAN SUSPENSION BRIDGE , 2001 .

[45]  Nicholas P. Jones,et al.  Inter-relations among flutter derivatives , 1997 .

[46]  Ahsan Kareem,et al.  Nonlinear response analysis of long-span bridges under turbulent winds , 2001 .

[47]  Grégory Turbelin,et al.  CFD calculations of indicial lift responses for bluff bodies , 2002 .

[48]  Guido Morgenthal,et al.  An immersed interface method for the Vortex-In-Cell algorithm , 2007 .

[49]  G. V. Parkinson,et al.  Phenomena and modelling of flow-induced vibrations of bluff bodies , 1989 .

[50]  Arindam Gan Chowdhury,et al.  Experimental identification of rational function coefficients for time-domain flutter analysis , 2005 .

[51]  Massimiliano Lazzari,et al.  Time domain modelling of aeroelastic bridge decks: a comparative study and an application , 2005 .

[52]  Ferruccio Resta,et al.  A new numerical approach to reproduce bridge aerodynamic non linearities in time domain , 2006 .

[53]  Tomomi Yagi,et al.  Vortex-induced vibration and its effect on torsional flutter instability in the case of B/D=4 rectangular cylinder , 2008 .

[54]  Hiroshi Sato,et al.  Comparative and sensitivity study of flutter derivatives of selected bridge deck sections, Part 1: Analysis of inter-laboratory experimental data , 2009 .

[55]  Gianni Bartoli,et al.  New developments in bridge flutter analysis , 2012 .

[56]  Santiago Hernández,et al.  THEORIES OF AERODYNAMIC FORCES ON DECKS OF LONG SPAN BRIDGES , 2000 .

[57]  T. K. Datta,et al.  Reliability Analysis of Suspension Bridges against Flutter , 2002 .

[58]  Nicholas P. Jones,et al.  COUPLED FLUTTER AND BUFFETING ANALYSIS OF LONG-SPAN BRIDGES , 1996 .

[59]  Hisato Matsumiya,et al.  New consideration on flutter properties based on step-by-step analysis , 2010 .

[60]  Tajammal Abbas,et al.  Assessment of Numerical Prediction Models for Aeroelastic Instabilities of Bridges , 2016 .

[61]  Xiang Hai-fan,et al.  Flutter control effect and mechanism of central-slotting for long-span bridges , 2007 .

[62]  Gang Chen,et al.  Flow-Oscillating Structure Interactions and the Applications to Propulsion and Energy Harvest , 2012 .

[63]  Xinjun Zhang,et al.  Investigation on aerodynamic stability of long-span suspension bridges under erection , 2004 .

[64]  Matthew E. Riley,et al.  Quantification of Model-Form, Predictive, and Parametric Uncertainties in Simulation-Based Design , 2011 .

[65]  Nicholas P. Jones,et al.  Coupled aeroelastic and aerodynamic response analysis of long-span bridges , 1996 .

[67]  Allan Larsen,et al.  Aeroelastic analysis of bridge girder sections based on discrete vortex simulations , 1997 .

[68]  Vincenzo Gattulli,et al.  Nonlinear Tuned Mass Damper for self-excited oscillations , 2004 .

[69]  I. E. Garrick On some reciprocal relations in the theory of nonstationary flows , 1938 .

[70]  Hiromichi Shirato,et al.  Aerodynamic derivatives of coupled/hybrid flutter of fundamental structural sections , 1993 .

[71]  Hiroshi Sato,et al.  Comparative and sensitivity study of flutter derivatives of selected bridge deck sections, Part 2: Implications on the aerodynamic stability of long-span bridges , 2009 .

[72]  A. Larsen,et al.  Two dimensional discrete vortex method for application to bluff body aerodynamics , 1997 .

[73]  Claudio Borri,et al.  Application of indicial functions in bridge deck aeroelasticity , 2006 .

[74]  J. N. Yang,et al.  Multimode Bridge Response to Wind Excitations , 1983 .

[75]  Hiromichi Shirato,et al.  The influence of aerodynamic derivatives on flutter , 1996 .

[76]  James M. W. Brownjohn,et al.  Strategies for aeroelastic parameter identification from bridge deck free vibration data , 2001 .

[77]  J. R. Banerjee,et al.  A simplified method for the free vibration and flutter analysis of bridge decks , 2003 .

[78]  Andreas G. Jensen Fluid dynamic derivatives: Marine and wind engineering approaches , 1997 .

[79]  Gianni Bartoli,et al.  Flutter mechanism for rectangular prisms in smooth and turbulent flow , 2006 .

[80]  Andrea Collina,et al.  Comparisons between wind tunnel tests on a full aeroelastic model of the proposed bridge over Stretto di Messina and numerical results , 1995 .

[81]  Ahsan Kareem,et al.  Advanced Structural Wind Engineering , 2013 .

[82]  K. Washizu,et al.  Aeroelastic instability of rectangular cylinders in a heaving mode , 1978 .

[83]  Koji Yamaguchi,et al.  Aerodynamics of wind effects on the Akashi Kaikyo Bridge , 1993 .

[84]  Giuseppe Vairo,et al.  A numerical model for wind loads simulation on long-span bridges , 2003, Simul. Model. Pract. Theory.

[85]  Xin Dabo,et al.  Numerical simulation of aerodynamic derivatives and critical wind speed for long-span bridges based on simplified steady wind field , 2007 .

[86]  Toshio Ueda,et al.  Aerodynamic simulation by CFD on flat box girder of super-long-span suspension bridge , 2001 .

[87]  Claudio Mannini,et al.  Flutter Vulnerability Assessment of Flexible Bridges , 2008 .

[88]  A. Kareem,et al.  AERODYNAMIC COUPLING EFFECTS ON FLUTTER AND BUFFETING OF BRIDGES , 2000 .

[89]  Masaru Matsumoto,et al.  The Complex Branch Characteristics of Coupled Flutter , 2006 .

[90]  Allan Larsen,et al.  Advances in aeroelastic analyses of suspension and cable-stayed bridges , 1998 .

[91]  Hiroshi Tanaka,et al.  Aerodynamic flutter analysis of cable-supported bridges by multi-mode and full-mode approaches , 2000 .

[92]  V. Boonyapinyo,et al.  Identification of Flutter Derivatives of Bridge Decks in Wind Tunnel Test by Stochastic Subspace Identification , 2009 .

[93]  Rimas Vaicaitis,et al.  Motion of Suspension Bridge Subject to Wind Loads , 1977 .

[94]  Suren Chen,et al.  Flutter reliability analysis of suspension bridges , 2005 .

[95]  Haifan Xiang,et al.  Identification of 18 Flutter Derivatives of Bridge Decks , 2000 .

[96]  Guido Morgenthal,et al.  Behaviour of very long cable-stayed bridges during erection , 2010 .

[97]  Francesco Ubertini,et al.  On the evaluation of bridge deck flutter derivatives using RANS turbulence models , 2013 .

[98]  Nicholas P. Jones,et al.  A methodology for the experimental extraction of indicial functions for streamlined and bluff deck sections , 2003 .

[99]  J. Michael R. Graham,et al.  Aeroelastic Modelling of Long-Span Suspension Bridges , 2011 .

[100]  Masaru Matsumoto,et al.  Grating effect on flutter instability , 2001 .

[101]  J B Pang,et al.  Investigation and Prevention of Deck Galloping Oscillation with Computational and Experimental Techniques , 2001 .

[102]  R. Scanlan,et al.  INDICIAL AERODYNAMIC FUNCTIONS FOR BRIDGE DECKS , 1974 .

[103]  Robert H. Scanlan,et al.  Role of Indicial Functions in Buffeting Analysis of Bridges , 1984 .

[104]  Ragnar Sigbjörnsson,et al.  Finite element formulation of the self-excited forces for time-domain assessment of wind-induced dynamic response and flutter stability limit of cable-supported bridges , 2012 .

[105]  Duc-Huynh Phan,et al.  Flutter and Buffeting Control of Long-span Suspension Bridge by Passive Flaps: Experiment and Numerical Simulation , 2013 .

[106]  M. Matsumoto,et al.  Torsional flutter of bluff bodies , 1997 .

[107]  Dong-Woo Seo,et al.  EFFECTS OF ERRORS IN FLUTTER DERIVATIVES ON THE WIND- INDUCED RESPONSE OF CABLE-SUPPORTED BRIDGES , 2013 .

[108]  Ragnar Sigbjörnsson,et al.  An alternative analytical approach to prediction of flutter stability limits of cable supported bridges , 2011 .

[109]  Masaru Matsumoto,et al.  Flutter stabilization and heaving-branch flutter , 1999 .

[110]  Takanori Ikeda,et al.  Prediction of aerodynamic characteristics of a box girder bridge section using the LES turbulence model , 2008 .

[111]  Yaojun Ge,et al.  Indicial Functions for Bridge Aeroelastic Forces and Time-Domain Flutter Analysis , 2011 .

[112]  Franco Bontempi,et al.  Comparison of time domain techniques for the evaluation of the response and the stability in long span suspension bridges , 2007 .

[113]  Nicholas P. Jones,et al.  Prediction of cable-supported bridge response to wind : coupled flutter assessment during retrofit , 2003 .

[114]  Robert H. Scanlan,et al.  Reexamination of sectional aerodynamic force functions for bridges , 2001 .

[115]  Ramana V. Grandhi,et al.  A Method for the Quantification of Model-Form and Parametric Uncertainties in Physics-Based Simulations , 2011 .

[116]  A. Kareem,et al.  Efficacy of Averaging Interval for Nonstationary Winds , 2014 .

[117]  A. Larsen,et al.  Discrete vortex simulation of vortex excitation and mitigation in bridge engineering , 2003 .

[118]  Holger Svensson,et al.  ANALYTICAL AERODYNAMIC INVESTIGATION OF CABLE-STAYED HELGELAND BRIDGE , 1992 .

[119]  Luca Caracoglia,et al.  Estimation of torsional-flutter probability in flexible bridges considering randomness in flutter derivatives , 2011 .

[120]  Hoyeop Lee,et al.  A Simplified Evaluation in Critical Frequency and Wind Speed to Bridge Deck Flutter , 2011 .

[121]  Luca Bruno,et al.  The validity of 2D numerical simulations of vortical structures around a bridge deck , 2003 .

[122]  R. D. Blevins,et al.  The Galloping Response of a Two-Degree-of-Freedom System , 1974 .

[123]  Robert H. Scanlan,et al.  Problematics in Formulation of Wind‐Force Models for Bridge Decks , 1993 .

[124]  Haifan Xiang,et al.  Parametric study on flutter derivatives of bridge decks , 2001 .

[125]  Young-Min Kim,et al.  Wind Engineering on the New Millennium Bridge in South Korea , 2011 .

[126]  Guido Morgenthal,et al.  Aerodynamic Behaviour of Very Long Cable-Stayed Bridges during Construction , 2010 .

[127]  Robert H. Scanlan,et al.  Interpreting Aeroelastic Models of Cable‐Stayed Bridges , 1987 .

[128]  Guido Morgenthal,et al.  A GPU-accelerated pseudo-3D vortex method for aerodynamic analysis , 2014 .

[129]  Ming Gu,et al.  Wind Tunnel and CFD Study on Identification of Flutter Derivatives of a Long‐Span Self‐Anchored Suspension Bridge , 2007, Comput. Aided Civ. Infrastructure Eng..

[130]  Wei Peng,et al.  Study on flutter characteristics of cable-supported bridges , 2003 .

[131]  T. Argentini,et al.  An experimental validation of a band superposition model of the aerodynamic forces acting on multi-box deck sections , 2013 .

[132]  Robert H. Scanlan,et al.  Some observations on the state of bluff-body aeroelasticity , 1997 .

[133]  R. Kurniawan Numerical Study of Flutter of a Two-Dimensional Aeroelastic System , 2013 .

[134]  Hiroshi Tanaka,et al.  Application of a reliability analysis model to bridge flutter under extreme winds , 2000 .

[135]  M. Vezza,et al.  Prediction of unsteady flow around square and rectangular section cylinders using a discrete vortex method , 1999 .

[136]  Claudio Borri,et al.  Non-stationary flow forces for the numerical simulation of aeroelastic instability of bridge decks , 2002 .

[137]  Alberto Zasso,et al.  Flutter derivatives: Advantages of a new representation convention , 1996 .

[138]  Luca Caracoglia,et al.  Application of random eigenvalue analysis to assess bridge flutter probability , 2015 .

[139]  Ahsan Kareem,et al.  Identification of critical structural modes and flutter derivatives for predicting coupled bridge flutter , 2008 .

[140]  Yao Jun Ge,et al.  Great Demand and Great Challenge: Chinese Major Bridges under Construction for Improving Traffic Infrastructure Nationwide , 2007 .

[141]  Piero D’Asdia,et al.  Aeroelastic instability of long-span suspended bridges: a multi-mode approach , 1998 .

[142]  Federica Tubino,et al.  Relationships among aerodynamic admittance functions, flutter derivatives and static coefficients for long-span bridges , 2005 .

[143]  Nicholas P. Jones,et al.  Effect of modal damping on bridge aeroelasticity , 1998 .

[144]  Bingnan Sun,et al.  Parametric study on the aerodynamic stability of a long-span suspension bridge , 2004 .

[145]  Christos T. Georgakis,et al.  Cable supported bridges concept and design , 2011 .

[146]  Santiago Hernández,et al.  Multidisciplinary approach to aeroelastic studies of long-span bridges , 2008 .

[147]  Pedro Albrecht,et al.  Finite Element‐Based Flutter Analysis of Cable‐Suspended Bridges , 1992 .

[148]  Alberto Zasso,et al.  Monte Carlo analysis of total damping and flutter speed of a long span bridge: Effects of structural and aerodynamic uncertainties , 2014 .

[149]  Herbert Wagner Über die Entstehung des dynamischen Auftriebes von Tragflügeln , 1925 .

[150]  Liu Ketong,et al.  Numerical Investigation for Aerodynamic Derivatives of Bridge Deck Using DES , 2014 .

[151]  Ahsan Kareem,et al.  AEROELASTIC ANALYSIS OF BRIDGES: EFFECTS OF TURBULENCE AND AERODYNAMIC NONLINEARITIES , 2003 .

[152]  Robert H. Scanlan,et al.  The action of flexible bridges under wind, I: Flutter theory† , 1978 .

[153]  T.J.A. Agar,et al.  Aerodynamic flutter analysis of suspension bridges by a modal technique , 1989 .

[154]  Robert H. Scanlan,et al.  MOTION-RELATED BODY-FORCE FUNCTIONS IN TWO-DIMENSIONAL LOW-SPEED FLOW , 2000 .

[155]  P. S. Brar,et al.  NUMERICAL CALCULATION OF FLUTTER DERIVATIVES VIA INDICIAL FUNCTIONS , 1996 .

[156]  Francesco Ubertini,et al.  Indicial functions and flutter derivatives: A generalized approach to the motion-related wind loads , 2013 .

[157]  Gianni Bartoli,et al.  Toward an Improvement in the Identification of Bridge Deck Flutter Derivatives , 2009 .

[158]  Ken Badcock,et al.  Propagation of structural uncertainty to linear aeroelastic stability , 2010 .

[159]  Allan Larsen,et al.  Aerodynamic aspects of the final design of the 1624 m suspension bridge across the Great Belt , 1993 .

[160]  Young-Min Kim,et al.  Coupled flutter analysis of long-span bridges using full set of flutter derivatives , 2015, KSCE Journal of Civil Engineering.

[161]  Yuguang Bai,et al.  Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and DES , 2010 .

[162]  Airong Chen,et al.  Coupled Flutter Analysis of Long-span Bridges by Multimode and Full-order Approaches , 2001 .

[163]  Kai-Uwe Bletzinger,et al.  Bridge flutter derivatives based on computed, validated pressure fields , 2012 .

[164]  Fumitaka Yoshizumi,et al.  An experimental approach on aerodynamic stability of a cable-stayed cantilever bridge , 2002 .

[165]  Claudio Borri,et al.  Aeroelastic phenomena and pedestrian-structure dynamic interaction on non-conventional bridges and footbridges , 2010 .

[166]  Shizhong Qiang,et al.  Weighting ensemble least-square method for flutter derivatives of bridge decks , 2003 .

[167]  W. M. Adams,et al.  Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization , 1984 .

[168]  Y. K. Lin,et al.  Stochastic Stability of Bridges Considering Coupled Modes: II , 1988 .

[169]  Uwe Starossek,et al.  Experimental and numerical identification of flutter derivatives for nine bridge deck sections , 2009 .

[170]  Ming Gu,et al.  Flutter- and buffeting-based selection for long-span bridges , 1999 .

[171]  T. Argentini,et al.  Aerodynamic instability of a bridge deck section model: Linear and nonlinear approach to force modeling , 2010 .

[172]  Guido Morgenthal Advances in Numerical Bridge Aerodynamics and Recent Applications , 2005 .

[173]  Nicholas P. Jones,et al.  Aeroelastic Analysis of Cable‐Stayed Bridges , 1990 .

[174]  Arindam Gan Chowdhury,et al.  A new technique for identification of eighteen flutter derivatives using a three-degree-of-freedom section model , 2003 .

[175]  Lin Zhao,et al.  Theoretical framework of feedback aerodynamic control of flutter oscillation for long-span suspension bridges by the twin-winglet system , 2015 .

[176]  Bert Blocken,et al.  50 years of Computational Wind Engineering: Past, present and future , 2014 .

[177]  E. S. Kreis,et al.  A NUMERICAL INQUIRY INTO THE FLUTTER PHENOMENON IN LONG-SPAN BRIDGES , 2005 .

[178]  Hiromichi Shirato,et al.  Flutter characteristics of H-shaped cylinders with various side-ratios and comparisons with characteristics of rectangular cylinders , 2008 .

[179]  T.J.A. Agar,et al.  Dynamic instability of suspension bridges , 1991 .

[180]  Luca Martinelli,et al.  Refined optimal passive control of buffeting-induced wind loading of a suspension bridge , 2014 .

[181]  Shambhu Sharan Mishra,et al.  Multimode flutter of long-span cable-stayed bridge based on 18 experimental aeroelastic derivatives , 2008 .

[182]  Giuseppe Vairo,et al.  A Simple Analytical Approach to the Aeroelastic Stability Problem of Long-Span Cable-Stayed Bridges , 2010 .

[183]  Yaojun Ge,et al.  Computational models and methods for aerodynamic flutter of long-span bridges , 2008 .

[184]  Allan Larsen,et al.  Prediction of aeroelastic stability of suspension bridges during erection , 1997 .

[185]  Kincho H. Law,et al.  Power evaluation of flutter-based electromagnetic energy harvesters using computational fluid dynamics simulations , 2014 .

[186]  Miguel A. Astiz,et al.  Flutter Stability of Very Long Suspension Bridges , 1998 .

[187]  Ahsan Kareem,et al.  A nonlinear analysis framework for bluff-body aerodynamics: A Volterra representation of the solution of Navier-Stokes equations , 2015 .

[188]  John S. Owen,et al.  Fluid–structure interaction of prismatic line-like structures, using LES and block-iterative coupling , 2008 .

[189]  Claudio Borri,et al.  Aeroelastic Wind Forces on Flexible Bridge Girders , 2000 .

[190]  Guido Morgenthal,et al.  Framework for sensitivity and uncertainty quantification in the flutter assessment of bridges , 2016 .

[191]  Virote Boonyapinyo,et al.  Advanced aerodynamic analysis of suspension bridges by state-space approach , 1999 .

[192]  Renato Vitaliani,et al.  Aeroelastic forces and dynamic response of long-span bridges , 2004 .

[193]  J. B Frandsen,et al.  Simultaneous pressures and accelerations measured full-scale on the Great Belt East suspension bridge , 2001 .

[194]  Allan Larsen,et al.  Discrete vortex simulation of flow around five generic bridge deck sections , 1998 .

[195]  Jong-Cheng Wu,et al.  Prediction of flutter derivatives by artificial neural networks , 2008 .

[196]  Ahsan Kareem,et al.  Bridge aerodynamics and aeroelasticity: A comparison of modeling schemes , 2013 .

[197]  Nicholas P. Jones,et al.  Multi-mode flutter and buffeting analysis of the Akashi-Kaikyo bridge , 1998 .

[198]  Sun Bing-nan,et al.  Aerodynamic stability of cable-stayed-suspension hybrid bridges , 2005 .

[199]  Yoshiyuki Daito,et al.  Torsional Flutter Mechanism of Two Edge Girders for Long Span Cable-Stayed Bridge , 2001 .

[200]  C. S. Cai,et al.  Determination of 18 Flutter Derivatives of Bridge Decks by an Improved Stochastic Search Algorithm , 2012 .

[201]  Haifan Xiang,et al.  Refinements on aerodynamic stability analysis of super long-span bridges , 2001 .

[202]  Masaru Matsumoto,et al.  Frequency Characteristics in Various Flutter Instabilities of Bridge Girders , 2001 .

[203]  Claudio Borri,et al.  Quasi-steady analysis of a two-dimensional bridge deck element , 2004 .

[204]  Lu Zhenzhou,et al.  Reliability and Sensitivity Analysis of Transonic Flutter Using Improved Line Sampling Technique , 2009 .

[205]  Ahsan Kareem,et al.  CURVE VEERING OF EIGENVALUE LOCI OF BRIDGES WITH AEROELASTIC EFFECTS , 2003 .

[206]  Ru-Cheng Xiao,et al.  Probabilistic free vibration and flutter analyses of suspension bridges , 2005 .

[207]  R. T. Jones The unsteady lift of a wing of finite aspect ratio , 1940 .

[208]  Hiromichi Shirato,et al.  Coupled flutter stability from the unsteady pressure characteristics point of view , 2011 .

[209]  R. C. Batista,et al.  Aerodynamic Stability Analysis of Cable-Stayed Bridges , 1995 .

[210]  A. Kareem,et al.  TIME DOMAIN FLUTTER AND BUFFETING RESPONSE ANALYSIS OF BRIDGES , 1999 .

[211]  M. Matsumoto,et al.  AERODYNAMIC DAMPING OF PRISMS , 1996 .

[212]  Hiromichi Shirato,et al.  Effects of aerodynamic interferences between heaving and torsional vibration of bridge decks: the case of Tacoma Narrows Bridge , 2003 .

[213]  Ahsan Kareem,et al.  Modeling hysteretic nonlinear behavior of bridge aerodynamics via cellular automata nested neural network , 2011 .

[214]  Haifan Xiang,et al.  Theoretical Model and Method for Self-Excited Aerodynamic Forces of Long-Span Bridges , 2009 .

[215]  Haili Liao,et al.  Identification of Flutter Derivatives of Bridge Deck Under Multi-Frequency Vibration , 2011 .

[216]  H. O. Madsen,et al.  Probabilistic flutter criteria for long span bridges , 1992 .

[217]  Masaru Matsumoto,et al.  Flutter and its application—Flutter mode and ship navigation , 2013 .

[218]  Krzysztof Wilde,et al.  Analytical study on flutter suppression by eccentric mass method on FEM model of long-span suspension bridge , 2001 .

[219]  M. Karpel,et al.  Design for active and passive flutter suppression and gust alleviation. Ph.D. Thesis , 1981 .

[220]  Guido Morgenthal,et al.  Parallels between wind and crowd loading of bridges , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[221]  S. Hernández,et al.  Sensitivity analysis of bridge flutter with respect to mechanical parameters of the deck , 2004 .

[222]  Herbert Werner,et al.  LMI‐based gain scheduling for bridge flutter control using eccentric rotational actuators , 2012 .

[223]  Xinzhong Chen,et al.  Improved Understanding of Bimodal Coupled Bridge Flutter Based on Closed-Form Solutions , 2007 .

[224]  Yozo Fujino,et al.  Identification of flutter derivatives of bridge deck from free vibration data , 1995 .

[225]  Zhang Zhe,et al.  Some new insights into the identification of bridge deck flutter derivatives , 2014 .

[226]  Emanuele Zappa,et al.  Complex aerodynamic admittance function role in buffeting response of a bridge deck , 2001 .

[227]  L. Patruno,et al.  Accuracy of numerically evaluated flutter derivatives of bridge deck sections using RANS: Effects on the flutter onset velocity , 2015 .

[228]  Shigeru Watanabe,et al.  Aerodynamic study of slotted box girder using computational fluid dynamics , 2008 .

[229]  Jin Cheng,et al.  Nonlinear aerostatic stability analysis of Jiang Yin suspension bridge , 2002 .

[230]  D. Peters Two-dimensional incompressible unsteady airfoil theory—An overview , 2008 .

[231]  Francesco Ubertini,et al.  On the identification of flutter derivatives of bridge decks via RANS turbulence models: Benchmarking on rectangular prisms , 2014 .

[232]  Alberto Zasso,et al.  Suspension bridge parameter identification in full-scale test , 1992 .

[233]  Toshio Miyata,et al.  Historical view of long-span bridge aerodynamics , 2003 .

[234]  Guido Morgenthal,et al.  Analysis of Aeroelastic Bridge Deck Response to Natural Wind , 2005 .

[235]  Dorian Janjic,et al.  Software Tool for Wind Design of Cable Stayed Bridges , 2008 .

[236]  Aitor Baldomir,et al.  Probabilistic optimization of the main cable and bridge deck of long-span suspension bridges under flutter constraint , 2015 .

[237]  Nicholas P. Jones,et al.  Time domain vs. frequency domain characterization of aeroelastic forces for bridge deck sections , 2003 .

[238]  Ragnar Sigbjörnsson,et al.  Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasi-steady theory: A case study , 2010 .

[239]  You-Lin Xu,et al.  Wind Effects on Cable-Supported Bridges: Xu/Wind Effects on Cable-Supported Bridges , 2013 .

[240]  John S. Owen,et al.  Application of the k―ω turbulence model for a wind-induced vibration study of 2D bluff bodies , 2009 .

[241]  Koichiro Fumoto,et al.  Full aeroelastic model test of a super long-span bridge with slotted box girder , 2001 .

[242]  S. Ariaratnam,et al.  Stability of Bridge Motion in Turbulent Winds , 1980 .

[243]  Piotr Omenzetter,et al.  Time domain formulation of self-excited forces on bridge deck for wind tunnel experiment , 2003 .

[244]  Ming Gu,et al.  Direct identification of flutter derivatives and aerodynamic admittances of bridge decks , 2004 .

[245]  Ragnar Sigbjörnsson,et al.  Time domain modeling of self-excited aerodynamic forces for cable-supported bridges: A comparative study , 2011 .

[246]  Robert H. Scanlan,et al.  AMPLITUDE AND TURBULENCE EFFECTS ON BRIDGE FLUTTER DERIVATIVES , 1997 .

[247]  Šarkić Anina,et al.  Numerical simulations and experimental validations of force coefficients and flutter derivatives of a bridge deck , 2015 .

[248]  Ming Gu,et al.  Determination of flutter derivatives by stochastic subspace identification technique , 2004 .

[249]  Robert H. Scanlan,et al.  Observations on Low-Speed Aeroelasticity , 2002 .

[250]  Ahsan Kareem,et al.  Multimode coupled flutter and buffeting analysis of long span bridges , 2001 .

[251]  Ahsan Kareem,et al.  Advances in modeling of Aerodynamic forces on bridge decks , 2002 .

[252]  F. Nieto,et al.  On the applicability of 2D URANS and SST k - ω turbulence model to the fluid-structure interaction of rectangular cylinders , 2015 .

[253]  Aitor Baldomir,et al.  Reliability based design optimization of long-span bridges considering flutter , 2014 .

[254]  H. Tanaka,et al.  Coupled mode flutter analysis using flutter derivatives , 1992 .

[255]  Paolo Spinelli,et al.  A discrete 3D model for bridge aerodynamics and aeroelasticity: nonlinearities and linearizations , 2007 .

[256]  K. Washizu,et al.  Aeroelastic instability of rectangular cylinders in a torsional mode due to a transverse wind , 1980 .

[257]  Claudio Mannini,et al.  Aerodynamic uncertainty propagation in bridge flutter analysis , 2015 .

[258]  Alberto Zasso,et al.  Nonlinear effects in sectional model aeroelastic parameters identification , 1992 .

[259]  Y. Fujino,et al.  Vibration Mechanisms and Controls of Long-Span Bridges: A Review , 2013 .