Study On Dynamic Stability Of Circular Arch By Differential Quadrature Method

Arch bridge has a long history in China, It is often used to all kinds of engineering practice with strong spanning ability, high bearing capacity, light structure, low cost, beautiful modelling and so on. Most of the current research has focused on the stability of circular arch subjected to static and most limited to theoretical derivation, and the circular arch of dynamic stability study is relatively less. On the basis of previous studies, this paper mainly uses the differential quadrature method to study the issue of static stability for linear circular arch which affected by radial loads and dynamic stability for linear circular arch which affected by radial cyclic loads .The main content of this article is as follows:(1) This paper concisely introduces the theory of differential quadrature method, the determination of the weight coefficient, the selection of the nodes and the treatment of the boundary conditions. With the flat section assumption, the circular arch deformation geometry relationship is build. Then, using the principle of virtual work has established the arch equation of general control by ignore the high order nonlinear term to obtain the control equations of the cross section of arch. By using the differential quadrature method to disperse the equations. At last, with Matlab, the influence of the parameters on vault displacement - load curve is discussed by the radial uniformly distributed load.(2) A linear motion differential equation of free vibration was established based on infinitesimal element method with a displacement function is the function of harmonic change over time to get the six order differential equation modes derivative. To analysis the arch in the first three order natural frequency with the change of circular arch radius with differential quadrature method. For the problem of dynamic stability of circular arch's radial cyclic loading,movement differential equation coefficient of implict time function (cycle) diffiences the characteristics of free vibration problems of the application of the differential quadrature method.Get diretly differential quadrature method only to the discrete equation of the space coordinates to make contains which just has time variable of ordinary differential equations with periodic coefficient; Then the state variable is introduced so flat the first order equation of state is obtained, and the method of implicit Runge-Kutta is used to solve the problem. According to the theory of Floquet, the influence of various parameters on the dynamic stability area of the arch is discussed.(3) Using the BEAM189 in ANSYS, a finite element software, simulated the arc arch of the two ends, and the modal analysis and transient dynamics analysis were carried out. The results of the simulation of finite element software are very close to the result of numerical analysis.