Linear and nonlinear aeroelastic analysis frameworks for cable-supported bridges

Based on the general framework of the linear thin airfoil theory, aeroelastic analysis of bridges has evolved over the last few decades in both time and frequency domains. As the bridge span increases, aeroelastic forces exerted on the evolving bridge deck cross-sections exhibit a clear departure from the linearized analysis framework that have been the basis of conventional schemes. This trend and observations of nonlinearity in the bridge aeroelasticity in wind-tunnel experiments have prompted the need for the development of a new general analysis framework attentive to both linear and nonlinear wind-bridge interactions. In this paper, the existing conventional linear and nonlinear analysis frameworks are first systematically reviewed with a focus on the study of the relationships among them. After analyzing the shortcomings of these conventional frameworks, two advanced nonlinear models, i.e., artificial neural network- (ANN-) and Volterra series-based models are introduced. The important parameters of conventional and advanced models are investigated in detail to emphasize the physical significance of these models in the simulation of the wind-bridge interactions. Application examples of the linear and nonlinear schemes are also presented highlighting the aeroelastic effects under smooth/turbulent wind conditions.

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

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

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

[4]  A. G. Davenport.  Buffeting of a Suspension Bridge by Storm Winds , 1962 .

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

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

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

[8]  Yuan-Cheng Fung,et al.  An introduction to the theory of aeroelasticity , 1955 .

[9]  M. Schetzen.  The Volterra and Wiener Theories of Nonlinear Systems , 1980 .

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

[11]  Atsushi Hirai,et al.  Aerodynamic Stability of Suspension Bridges , 1949 .

[12]  H. W. Liepmann,et al.  On the Application of Statistical Concepts to the Buffeting Problem , 1952 .

[13]  Claudio Borri,et al.  Frequency- and time-domain methods for the numerical modeling of full-bridge aeroelasticity , 2007 .

[14]  R. L. Halfman.  Experimental aerodynamic derivatives of a sinusoidally oscillating airfoil in two-dimensional flow , 1952 .

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

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

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

[18]  Ahsan Kareem,et al.  Modelling of nonlinear bridge aerodynamics and aeroelasticity: a convolution based approach , 2012 .

[19]  K. McKee.  Book Reviews : Wind Effects On Structures: E. Simiu and R.H. Scanlan John Wiley & Sons, New York, New York 1980, $33.50 , 1981 .

[20]  Pol D. Spanos,et al.  Non-linear multi-degree-of-freedom system random vibration by equivalent statistical quadratization , 1992 .

[21]  山田 均,et al.  Long-span bridges and aerodynamics , 1999 .

[22]  Friedrich Bleich,et al.  Dynamic Instability of Truss-Stiffened Suspension Bridges under Wind Action , 1949 .

[23]  R H Scanlan,et al.  STATE-OF-THE ART METHODS FOR CALCULATING FLUTTER, VORTEX-INDUCED, AND BUFFETING RESPONSE OF BRIDGE STRUCTURES , 1981 .

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

[25]  C.P.W. Geurts,et al.  Proceedings of the 13th international conference on wind engineering (ICWE13), July 10-15, 2011, Amsterdam , 2011 .

[26]  R. Scanlan,et al.  Experimental Aerodynamic Coefficients in the Analytical Study of Suspension Bridge Flutter , 1969 .

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

[28]  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 .

[29]  Earl H. Dowell,et al.  Nonlinear Aeroelasticity and Unsteady Aerodynamics , 2002 .

[30]  Ahsan Kareem,et al.  Stochastic response of tension leg platforms to wind and wave fields , 1990 .

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

[32]  Giorgio Diana,et al.  Experience gained in the Messina bridge aeroelastic project , 1998 .

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

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

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

[36]  Robert H. Scanlan,et al.  AIR FOIL AND BRIDGE DECK FLUTTER DERIVATIVES , 1971 .

[37]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[38]  V. Denoël.  Limit analysis of the statistics of quasi-steady non-linear aerodynamic forces for small turbulence intensities , 2009 .

[39]  W. Silva,et al.  Discrete-time linear and nonlinear aerodynamic impulse responses for efficient cfd analyses , 1997 .

[40]  W. Sears,et al.  Some Aspects of Non-Stationary Airfoil Theory and Its Practical Application , 1941 .

[41]  W. Rugh.  Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .

[42]  A. Kareem,et al.  Wind-induced effects on bluff bodies in turbulent flows: Nonstationary, non-Gaussian and nonlinear features , 2013 .

[43]  Vito Volterra,et al.  Theory of Functionals and of Integral and Integro-Differential Equations , 2005 .

[44]  Elias B. Kosmatopoulos,et al.  Analysis and modification of Volterra/Wiener neural networks for the adaptive identification of non-linear hysteretic dynamic systems , 2004 .

[45]  Walter Lacarbonara,et al.  Nonlinear parametric modeling of suspension bridges under aeroelastic forces: torsional divergence and flutter , 2012 .

[46]  N. Wiener,et al.  Response of a Non-Linear Device to Noise , 1942 .

[47]  N. P. Jones,et al.  Identification of aeroelastic parameters of flexible bridges , 1994 .

[48]  Ahsan Kareem,et al.  Modeling Nonlinear Systems by Volterra Series , 2010 .

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

[50]  Ahsan Kareem,et al.  Equivalent Statistical Quadratization and Cubicization for Nonlinear Systems , 1997 .

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

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

[53]  Glenn B. Woodruff,et al.  The Failure of the Tacoma Narrows Bridge , 1941 .

[54]  Ahsan Kareem,et al.  Stochastic response of a tension leg platform to viscous and potential drift forces , 1994 .

[55]  Ahsan Kareem,et al.  The effects of turbulence on the pressure distribution around a rectangular prism , 1998 .

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

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

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