Efficient Algorithm For Bridge Dynamic Responses Considering Multiple Support Excitation And Wave-passage-damping Phenomenon

With the fast development in the coastal area and the outburst of new infrastructures in the west region,bridges springing up across China.The lifeline system is extremely important during earthquake disasters.The damaged bridges after earthquakes stopped the rescue troops and the material from entering the disaster area,causing indirect casualties and vast economic losses.The anti-seismic design of large span bridges,high pier bridges and special-shaped bridges are important research fields in civil engineering and the effect of multiple support excitation(MSE)is an topic that can not be crossed for the researchers.As has been concluded from existing studies,the structural form,span,stiffness and direction of a bridge are essential factors that affect its seismic responses.These factors are decided during the initial design phase.Existing design codes consider MSE in the phase of seismic check when little can be done to these essential factors.Considering MSE in the initial design phase can both increase the anti-seismic capability and economic efficiency of a bridge.To achieve this goal,accurate modeling are indispensable,efficient algorithms are essential in screening designing plans of massive amount,a deep understanding of the mechanism of MSE effect is crutial in exploring its advantagous aspects.Consequently,in this article,systematic and in-depth studyies are carried out forcusing on the structural modeling method,efficient statistical algorithms and the mechanism of the MSE effect.(1)In order to accurately calculate the responses of multiple support bridges,and integrate the results obtained by different modeling methods from existing studies.The definition of virtual damping error is made.The virtual damping error is caused by using unreasonable damping formulating methods and changes with the changing of reference coordinates.The results from the large mass method(LMM)approaches the true responses of the structure when the large masses approaches infinity.This property is used to derive the limit equation of motion of the LMM,and is named as displacement-velocity method(DVM).This method is simple in expression and has physical significance.the RMM is proved to be equivalent to the DVM.The response of the rigid body modes and the supports'relative motion modes are proved to approach the pseudo-static response in the relative motion method(RMM)giving physical significance to the RMM.Moreover,the virtual damping error and the damping truncation error caused by using the Rayleigh damping method instead of the modal damping method in the RMM,the LMM and the absolute displacement method are studied.Theoretical derivation shows that virtual damping error doesn't exist in the RMM.A new Rayleigh damping formula for the LMM is proposed that can eliminate the virtual damping errors in the LMM.The mechanism of how the errors are influenced by the effect of MSE are studied both theoretically and numerically.(2)In order to meet the requirements of accuracy and efficiency in screening large amounts of design plan,an efficient time-domain algorithm used for nonstationary random analysis is developed.The drifting problme of the displacement signal,obtained from twice integrating the corresponding nonstationary acceleration signal which is generated by directly multiplying a time modulating functions with a stationary acceleration signal,is solved in this algorithm.The earthquake-structure augmented system is first assembled and then reduced with the strategy of one-output-each-system.The efficiency of the algorithm is significantly increased without losing accuracy by using this strategy.Taking advantage of the efficiency and accuracy of the Lyapunov equation solving algorithms and by using parallel computation,the algorithm is competent as an efficient tool for solving nonstationary MSE structural responses.(3)To explore the positive aspects of the MSE effect for anti-seismic design,the DVM is used in analyzing the mechanism of MSE.During the analysis,a phenomenon aroused by the structural dampings and the wave passage effect is observed.In symmetrical structures,the two elements at symmetical positions usually don't have the same response.This phenomenon is named as wave-passage-damping(WPD)effect in this article.This defination is then extended to non-symmetrical structures.Under the influence of the WPD effect,the elements at the symmetrical position of a structure cannot usually have the same response in the same eqrthquake event.The element having the smaller response can share its anti-seismic storage with the element having the larger response,under certain control.WPD effect provides a sound theoritcal basis for asymmetrical design and for carrying out asymmetrical control according to the incident angle of a coming earthquake.The mechanism of MSE effect and the WPD effect are testified with a Benchmark cable-stayed bridge.Numerical results show that the WPD effect exists in both large span and short span bridges and is prominent enough for practical use.(4)To testify the rationality and validty of the theoretical and numerical conclusions,experiments are carried out with a simple supported beam mounted with masses.The control variable method is used for the design of experiments.Spectrum analysis and variance analysis are used proved the conclusions obtained from mechanism study.Expriments are also desiged for the WPD effect.Results show the existence of the WPD effect in the beam,which can be as large as 42% of its total responses.