Wave Spectral Quasi Analytical Model And Rapid Calculation Of Train-Induced Vibration In Over-Track Buildings Of Metro Depot

With the metro depot over-track buildings getting booming,problems of vibration and noise are becoming more and more important.There are lots of new challenges for the over-track buildings,such as the change of vibration source characteristics,unclear propagation path mechanism,lack of vibration and noise emission standards,etc.These new challenges have made it difficult to predict the vibration and noise in buildings and to give a proper method to attenuate the vibration and noise.To solve these problems,knowing the theory that how does the vibration transmit through the buildings is important.Considering the above problems,a wave spectral quasi analytical method has been developed.By focusing on the theory of vibration transmission,this paper has achieved a fast prediction method,which has been used to study the vibration transmission rules from the aspects of building characters,structure modes,response spectrum,etc.This study has also provided a method of achieving the reference basis for the environmental vibration emission standard of the depot.With the support of National Natural Science Foundation of China,“Study of prediction accuracy and reliability of train-induced vibration and its environmental influence(No.51778049)” and Beijing Municipal Natural Science Foundation,“Study of the exposure-response relationships for resident annoyance caused by building vibration and secondary noise from metro trains(No.8202040)”,this paper has optimized the modeling of periodic frame structures from both of the aspects of component and structure.The relation between the wave and vibration in the periodic structures was studied,according to which the wave spectral quasi analytical model of the periodic multi-span over-track buildings was established.With the wave spectral quasi analytical model,this paper calculated the data base of the response transfer function(RTF)from the base of the over-track buildings to the rooms of each floors in the building.According to the RTF data base,the transmission rules of the vibration in buildings was studied.In addition,the method of calculating the limit vibration value of the platform of the metro depot according to the limit value of rooms was obtained.The main research contents,results and innovations are as follow:(1)Spectral element model of beam-plate-column coupling structure has been established.Dynamic shape functions of beam/bar components are derived under axial,torsional and bending vibration condition,individually,which form the spectral element model of the beam/bar structures.By decomposing the rectangular thin plate into two quasi one-dimensional plate problems under bending deformation,the spectral element model of rectangular plate with arbitrary boundary conditions is established.The spectral element method has been applied to the beam-column-plate coupled structure,which has made it possible to do the study of the dynamic properties of the frame structures.By using the spectral element method,only the necessary coupling nodes are needed,which means there is no need to set the additional nodes inside the uniform components.(2)The wave-spectral element model of periodic frame structure has been established.The cell structure was composed of beams,plates and columns.It is established by using spectral element method.According with the Floquet theory,the waves and the corresponding wave modes has been calculated by solving the characteristic equation.For a finite periodic structure,by applying periodic boundary conditions at the boundary of the cell,the vibration response of finite periodic structure has been calculated by the wave superposition method.In this way,the number of dofs of the overall structure can be reduced to the number of dofs in one cell,which can greatly improve the computational efficiency.Through the analysis of typical waves in the structure,an important conclusion has been obtained,which is that the axial vibration of a single span periodic frame structure is mainly composed of four main waves with different typical modes.(3)Wave spectral quasi analytical model of multi-span periodic over-track building has been proposed and established.The vibration problem of over-track buildings could be reduced to the dynamic calculation of the typical span structures.If the horizontal boundaries of the typical span structures at each floor are similar,the multi-span structure can be abstracted as a "single span grilled fish fillet" structure containing 4pairs of characteristic waves by the inverse analysis method.The cell mode of the "single span grilled fish fillet" has been calculated by wave spectral element method.Then the wave spectral quasi analytical model is established.In this way the calculation was focused on the typical span,which achieved the rapid prediction of the vibration response in multi-span structures.(4)With the wave spectral quasi analytical model,the response transfer function database reflecting both structural characteristics and frequency division transmission characteristics has been established,which made it possible to predict the vibration of any height of rooms in over-track residential buildings rapidly.Based on the database,the transmission law and main influence factors of building vibration has been analyzed,and the method of calculating the limit vibration of the platform has been studied.These are useful for predicting the vibration and noise on the over-track buildings,optimizing the layout of the structures and designing the vibration and noise attenuation measures.