{"references": ["P. Anagnostopoulos, P.W. Bearman, \"Response characteristics of a\nvortex-excited cylinder at low Reynolds number,\" J. luids.Struct., vol. 6,\npp. 39-50, 1992.", "A. Khalak, C.H.K. Williamson, \"Investigation of the realative effects of\nmass and damping in vortex-induced vibration of a circular cylinder\", J.\nWind Eng. Ind. Aerodyn. vol. 69-71, pp. 341-350, 1997.", "D. Brika, A. Laneville, \"Vortex-induced vibrations of a long flexible\ncircular cylinder\", J. Fluid Mech. vol. 250, pp. 481-508, 1993.", "C.H.K. Williamson, A. Roshko, \"Vortex formation in the wake of an\noscillating cylinder\", J. Fluids Struct. vol. 2, pp. 355-381, 1988.", "E. Guilmineau, P. Queutey, \"Numerical simulation of vortex-induced\nvibration of a circular cylinder with low mass-damping in a turbulent\nflow\", J. Fluids Struct. vol. 19, pp. 449-466, 2004.", "S. Dong, G.E. Lesoinne, \"DNS of flow past a stationary and oscillating\ncylinder at Re=10000\", J. Fluids Struct. vol. 20, pp. 519-531, 2005.", "H. Al-Jamal, C. Dalton, \"vortex induced vibrations using large eddy\nsimulation at a moderate Reynolds number\", J. Fluids Struct. vol. 19, pp.\n73-92, 2004.", "A. Placzek, J.F. Sigrist, A.Hamdouni, \"Numerical simulation of an\noscillating cylinder in a cross-flow at low Reynolds number: Forced and\nfree oscillations\", Comuter&fluids. vol. 38, pp. 80-100, 2009.", "C.Y.Zhou, C.Sorm, K.Lam, \"vortex induced vibrations of an elastic\ncircular cylinder\", J. Fluids Struct. vol. 13, pp. 165-189, 1999.\n[10] G.W. Li, A.L. Ren, W.Q. Chen, \"An ALE method for vortex-induced\nvibrations of an elastic circular cylinder\", Acta.Aerodynamic.Asinica. vol.\n22, pp. 283-288, 2004.\n[11] J.R. Meneghini, P.W. Bearman, \"Numerical simulation of high amplitude\noscillatory flow about a circular cylinder\", J. Fluids Struct. vol. 9, pp.\n435-455, 1995.\n[12] T.Sarkaya, \"Hydrodynamic damping, flow-induced oscillations, and\nbiharmonic response\", ASME J.Offshore Mech. Arctic Eng. vol. 117, pp.\n232-238, 1995.\n[13] C.H.K. Williamson, R. Govardhan, \"Vortex-induced vibration\". Annu.\nRev. Fluid Mech. vol. 36, pp. 413-455, 2004.\n[14] T.E.Tezduyar , S.Mittal and S.E.Ray, \"Incompressible flow computations\nwith bilinear and linear equal-order-interpolation velocity-pressure\nelements\", Comp. Meth. App. Mech.&Eng., vol. 95, pp 221-242, 1992.\n[15] T. Li, J.Y. Zhang, W.H. Zhang. \"Efficient evaluation of space-time finite\nelement method\", Journal of Southwest Jiaotong Unversity, vol. 43. pp\n772-777. 2008\n[16] W.M. Zhai, Vehicle-track coupling dynamics. Beijing: China Railway\npublishing house, 2001, pp 397-399.\n[17] M. Mistsuhiro, N.Kazuhiro, M. Kisa, \"Unstructured dynamic mesh for\nlarge movement and deformation\", AIAA, vol. 40. pp 1-11. 2002\n[18] L.P. Franca, S.L. Frey, \"Stabilized finite element method:\nII. The incompressible Navier-Stokes equations\", Comp.\nMeth. App. Mech. & Eng., vol. 99. pp 209-233. 1992."]}

A numerical simulation of vortex-induced vibration of a 2-dimensional elastic circular cylinder with two degree of freedom under the uniform flow is calculated when Reynolds is 200. 2-dimensional incompressible Navier-Stokes equations are solved with the space-time finite element method, the equation of the cylinder motion is solved with the new explicit integral method and the mesh renew is achieved by the spring moving mesh technology. Considering vortex-induced vibration with the low reduced damping parameter, the variety trends of the lift coefficient, the drag coefficient, the displacement of cylinder are analyzed under different oscillating frequencies of cylinder. The phenomena of locked-in, beat and phases-witch were captured successfully. The evolution of vortex shedding from the cylinder with time is discussed. There are very similar trends in characteristics between the results of the one degree of freedom cylinder model and that of the two degree of freedom cylinder model. The streamwise vibrations have a certain effect on the lateral vibrations and their characteristics.