| In physical engineering, many structures are usually influenced by dynamical load following with time, such as nuclear power stations,large dams and high architectures enduring earthquake load,offshore structures enduring impact of ocean wave. To enssure the structures to work normally and safely, dynamical analysis is a necessary topic during design. Under the function of vehicle moving load, individual crowd moving load,wind force and earthquake ground movement,inner force in the bridge structure will exceed that calculated under the action of static force because of vibration, and partial fatigue damage of structure maybe occur, then vibration transmutation and acceleration which affect comfort and safety of vehicles moving on the bridge will come into being,even the bridge will be destroyed completely. In short the vibration is one of the important factors that affect safety and usage of bridge.Now the analysis of bridge vibration has already been applied to various domain of bridge engineering extensively, but for all the analyses the dynamic properties of natural frequency and modal must be confirmed first. Utilize the certain relation between natural frequency and stiffness,mass,we can avoid coupling between the vibration fountain frequency of forced vibration–wind, vehicle etc and natural frequency of the bridge at design stage,for example anti- wind calculation,anti- earthquake calculation and vehicle- bridge vibration analysis in dynamic analysis of bridge. In recent years the diagnosis bridge disease is also according to the change of natural frequency,so it is very important to confirm the natural frequency and model accurately. In the course of bridge design,to accomplish geometric dimension and material design considering dynamic loads,designers sometimes need to know the maximal response under worst-case behavior to guarantee safe reliability of the design. At present,computing dynamics of bridge structure is mainly based on finite element method(FEM),that is dynamic finite element method (DFEM). The FEM has been developed to a mature numerical method to resolve static and dynamic problems. But on the other hand, with the rapid development of science and technology and economic,large numbers of new style structures abounded. At the same time,FEM theory was studied profoundly. Researchers found that traditional FEM was invalid when dealt with nonlinear,large deformation,high stress gradient and structural dynamic metamorphosation which challenged the actual engineering design and analysis. The reason is that the FEM is founded on element grids. When encountering problem of remesh and distortion elements,the FEM is invalid.EFM is a numerical analysis method solving boundary value problem blossoming in recent decades of years. The most difference between EFM and traditional Finite element method(FEM) is that FEM is based on Lagrange interpolation to construct displacement function,while the EFM fits the field function using moving least square method chiefly ground on node coordinates. The interpolation of EFM is nonlinear. The direct mathematics bases of EFM are moving least square method (MLSM). The continuous function established on MLSM fits the field function of EFM. Such function has high-order continuity. As only series of discrete nodes are needed in whole solution domain,partial differential equation and integration are solved based on no information of elements. So grids are entirely avoidable. Or sometimes cells are auxiliary for integration. When faced some nonlinear and dynamical problems,EFM doesn't need initial mesh generation and remeshing. So the pre-treatment is greatly simplified. Simultaneously,the EFM avoids computation divergence happening for element distortion.The primary work in this paper is: firstly introducing EFM research development situation in domestic and foreign. In fact, thought of the EFM produced retrospect to the seventies last century from research of finite difference method of irregular node. For the sake of unprecedented recognition of FEM, the EFM had no development at that time. Until 1977,Lucyt and Gingold respectively brought forward Smoothed Particle Hydrodynamics,simplified as SPH,and successfully applied to the field of astrophysics. EFM began to become more and more popular. This paper mainly studies the application of EFM in bridge structure dynamic analysis. The EFM is in the ascendant in structural dynamical analysis. Based on Element Free Galerkin Method,this paper demonstrates mechanics and mathematics fundamentals involved in EFM including moving least square(MLS) technology and Gram-Schmidt normal orthonormalization,derives governing equations according to energy variation principle,expounds the basis function styles and its construction and three often used methods to impose essential boundary conditions::Lagrange multiplier method,coupled with FEM and penalty function method. Secondly,the paper introduces general steps to compute dynamic problems of bridge such as dynamic properties and response. As an example,the paper computes the dynamic properties of simply -supported beam bridge. In actual bridge structure analysis,vehicles on bridge often simplified as moving concentrated loads. However in numerical calculations,it is hard to discrete the concentrated loads to nodal loads. Linear interpolation and Hermite two-node interpolation often used in FEM.But it can't truly describe characteristics of moving concentrated loads. The weight-based shape function of EFM is applied to fit the loads and corresponding numerical analyses are carried out. Finally,the form of weight function and the principle of its parameters selection as well as computation precision are also analyzed in last chapter of this paper.Results in this paper show that it is reasonable and feasible to compute bridge vibration by EFM and it is rather easier to get satisfactory results. The method also has merits of simply data processing and high-order continuity of solution and will have a good prospect of practical application and research.
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