Investigation On Nonlinear Flutter And Post Flutter Robustness Of Long Span Bridges

Theoretically,long-span bridges would never experience flutter if the windresistant design is performed in strict accordance with the current flutter fortification standard.However,with increasing lengths of bridge-span,it may fail to meet the current flutter fortification standard in design;in the other hand,the non-stationary,adverse effects of the global climate change could further increase the possibility of flutter instability during the service stage.Therefore,it is of great significance to carry out researches on the post-flutter performances of long-span bridges.In this paper,the post-flutter response properties and robustness of a long-span suspension bridge are comprehensively studied by means of theoretical analysis,numerical simulation and finite element calculation.Main contents of this paper are as follows:(1)Indicial functions(IFs)are adopted to establish the time-domain self-excited loads model of the bridge deck,and the genetic optimization algorithm is proposed to achieve the rapid fitting of the parameters of indicial functions,and the accuracy of the time-domain self-excited loads model is verified.A method of deduction of the pseudosteady self-excited loads from the IFs-denoted aerodynamic loads is proposed to address the time-domain incompatibility between the mean wind loads and the selfexcited loads,and thus,an integrated time-domain aerodynamic model,which includes simultaneously the mean wind loads and the self-excited loads,is established successfully.(2)The concept of the multi-stage indicial functions is introduced to describe the nonlinear effects of self-excited loads in terms of motion amplitudes.In the timedomain procedure of flutter,the Indicial function corresponding to any intermediate amplitude can be obtained by interpolating within the adjacent two-stage indicial functions.The nonlinear self-excited loads model obtained by interpolation algorithm can not only accurately describe the evolving properties of the self-excited loads of the bridge deck,but also avoid the non-physical transient response induced by a sudden switch between two groups of indicial functions.(3)The time-domain analysis for the whole process of flutter of a suspension bridge is performed.Based on the numerical results,the post-flutter response properties,such as the evolution of the motion amplitudes,and of amplitude-and frequency-properties of the limit cycle oscillations(LCOs)with wind speeds,are summarized.The influences of the geometrical nonlinearities,aerodynamic nonlinearities and mean wind effects on the flutter thresholds and the post-flutter characteristics are investigated respectively.Numerical results show that these three kinds of effects mentioned above have little effects on the critical wind speed of flutter.However,they influence significantly post-flutter performances.Compared with the divergence oscillation revealed by the linear theory,geometric nonlinearities limit the development of the motion amplitudes,and eventually drive the bridge deck to a LCO of a much smaller amplitude.Furthermore,the aerodynamic nonlinearities and mean wind effects have remarkable effects on the LCO properties.(4)The linear flutter and post-flutter properties of four typical bridge-deck sections are investigated.Numerical results show that the segregated twin-box section is of the best flutter stability;the streamlined box and ?-shaped section are both rather good;the H-shaped section,however,is of the worst.The flutter instability of the Hshaped section manifests in single-torsional motion,and those of the remaining three sections are of obvious bending-torsional coupled feature.There are evident differences in post-flutter properties among these four kinds of typical cross-section.(5)The post-flutter robustness of the suspension bridge is studied.The fatigue performances of the key parts of the structure are taken as the assessment indicator of the robustness.For the stresses of the cross section of the main-girder and the bridge towers,the concept of Mises equivalent stress is introduced to normalize their complicated stresses,and the time-histories of the modified Mises equivalent stress are eventually obtained by the sign correction.For the cable components,including main cables,hangers and central ties,their tensile stresses time-histories are extracted directly by ANSYS post-processing.According to the stress condition of the key parts,the weaknesses of the bridge are determined and then corresponding fatigue strength and fatigue life estimation are performed.In addition,the evolution law of the fatigue properties of the weak members with the wind speed are studied.The analytical results show that the fatigue life of the key parts decreases rapidly as the wind speed increases,and the fatigue life of the central ties is always the minimum.Based on the calculation results of the maximum torsional amplitude of the bridge deck and the maximum stress of the central ties,the maximum torsional amplitude required for the strength fracture of the central ties is estimated,and at last compared with the flutter instability of the original Tacoma suspension bridge.