Nonlinear Aerodynamics And Wind-Induced Vibrations Of Bridge Decks

As the increasing span-length and innovative structural design of modern bridges make them more sensitive to wind-induced vibrations,the wind-resistant ability becomes one of the key factors that dominates the structural safety and normal operation of bridges.The wind-induced loads on bridge decks,towers,arch ribs,and hangers exhibit significant nonlinear features due to the bluff nature of their aerodynamic configurations.In the present paper,existing researches related to nonlinear bridge aerodynamics and wind-induced vibrations of bridge decks are reviewed and discussed;three important issues,i.e.,the nonlinear features of aerodynamic forces,the mathematical modeling of nonlinear aerodynamics,and the control of nonlinear wind-induced vibrations,are investigated.The main contents and some important conclusions are summarized as follows:(1)The mechanical stiffness and damping coefficients of spring-suspended bridge deck sectional models were conventionally extracted through free decay vibration tests in still air.The extracted stiffness and damping coefficients,indeed,include both mechanical and aerodynamic components.In the present work,an experimental procedure is designed to separate the mechanical and aerodynamic parameters of spring-suspended bridge deck sectional models.Vertical and torsional single-degree-of-freedom free vibration tests of two typical bridge deck section models are carried out in still air to study their nonlinear vibration characteristics.It is demonstrated that the damping of a spring-suspended section model in still air includes significant aerodynamic components;for wind tunnel tests with large-amplitude vibrations,the effect of aerodynamic components should be excluded in order to increase the accuracy of the identified mechanical damping ratio.The vibration frequency of a spring-suspended section model is lower than its natural frequency due to the effect of added mass(moment of inertia);for an ordinary bridge deck sectional model,the vibration frequency in still air is 1%?3%lower than its natural frequency.(2)The post-flutter limit cycle oscillation(LCO)of a two-degree-of-freedom bridge deck section model involving aerodynamic nonlinearities is simulated using computational fluid dynamics(CFD)simulations.To investigate the global aerodynamic mechanism for the post-flutter LCO,a comprehensive energy budget analysis is conducted based on the simulated responses,in which the energy input properties and hysteresis features of the 1st-order and higher-order force components are considered separately.It is demonstrated that that only the 1st-order force components contribute significantly in the energy input,while the contributions of the higher-order force components are insignificant;in the amplitude-increasing stage of post-flutter vibration,the phase differences between displacement and self-excited force signals vary remarkably,indicating that the aerodynamic derivatives may vary with the vibration state;the post-flutter response of bridge decks can be well simulated by considering only the 1st-order nonlinear components of the self-excited forces.(3)A describing function(DF)-based model is introduced to simulate the nonlinear bridge aerodynamics.The aerodynamic DFs(ADFs)can be either identified using the forced vibration technique or based on the free vibration response history.The accuracy of the DF-based model in simulating vortex-induced vibration and post-flutter vibration of bridge decks are verified by comparing the ADF-based results with reference results based on wind tunnel tests,CFD simulations,and several phenomenological models.It is demonstrated that the DF-based model can accurately capture typical features of vortex-induced vibration and post-flutter vibration,e.g.,LCO and hysteresis phenomena;and that the ADFs are insensitive to some structural dynamic parameters,e.g.,Scruton number.The ratio between the VIV amplitude of a flexilbe beck(at the position with the maximum amplitude)and that of a rigid bridge deck with the same structural parameters is dependent on the mode shape and mechanical damping ratio.The ratio obtained by Scanlan's VIV model is smaller than that obtained by the DF-based model.(4)The galloping and flutter instabilities of bridge decks have been conventionally examined in terms of the critical wind speed without considering the post-critical safety redundancy.To this end,thresholds for acceptable post-critical vibrations are defined accordingly to available limit states of vibration in literatures and design codes.Two simple indices,i.e.,the wind speed extension after the critical state with acceptable post-critical vibrations and the relative post-critical capacity(i.e.,the ratio between the aforementioned wind speed extension and the critical speed value),are utilized to quantify the post-critical performance of bridge decks.The effects of various mechanical and aerodynamic properties(e.g.,mechanical damping ratio,natural frequency,initial angle of attack,and aerodynamic derivatives)on the post-critical behaviors of three selected cross-sections are highlighted.It is demonstrated that the ratio between the safety wind speed extension after critical state and linear stability range may be as high as 10%~20% for the concerned sections.The quantitative analysis of post-critical performance in the present work may facilitate selecting effective measures to improve the post-flutter performances of a bridge at the preliminary design stage,and deepen the understanding of the wind-resistant performance of bridges.(5)The conventional target for self-excited galloping/flutter control focuses on the critical wind speed,and the optimization of tuned mass damper(TMD)parameters has been limited in a linear framework,in which only the linear part of the aeroelastic force is considered.In the present work,a new control target is introduced,i.e.,to ensure the vibration amplitude to be lower than a threshold value(pre-specified according to the expected structural performance)before a target wind speed is achieved.Unlike the conventional control target,the new one can take into account the underlying large-amplitude vibrations before the critical state and/or the structural safety redundancy after the critical state.To obtain the most economical TMD parameters that enable the new target,an optimization procedure involving nonlinear aeroelastic effect is developed for galloping control based on the quasi-steady aeroelastic force model,and for flutter control based on a nonlinear unsteady model.Four numerical examples involving the galloping/flutter control of different cross-sections are analyzed to highlight the superiorities of the new control target relative to the conventional one.It is demonstrated that the new target and optimization procedure can lead to more economical design results than the conventional ones in the galloping/flutter control for a structure with relatively large post-critical safety redundancy,and they are more reliable than the conventional ones for a structure that may experience large-amplitude vibrations(in case with sufficiently large external excitations)before the critical wind speed.These superiorities of the new control target and optimization procedure suggest that they may be utilized in the TMD parameter optimization for galloping/flutter control of structures in a wide domain of engineering fields.