1 State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact,PLA University of Science and Technology, Nanjing, 210007;
2. School of Mechanical Engineering , Nanjing University of Science and Technology , Nanjing , 210094
Abstract：The boundary conditions of circular arches in practical engineering can not be always simplified as perfect hinged or fixed ends.In order to study the influence of elastic support for the free vibration characteristics of circular arch,the variables such as force and displacements werenondimensionalized.According to the balance equation and coordinate conversion,the boundary conditions of arches with vertical ,horizontal and rotational elastic supports were obtained in polar coordinates.And the flexural and axial deformations were considered while shear deformations and rotation inertia were neglected in the governing equations of motion.The solutions of the governing equations under the boundary conditions are the functions only about the rise to span ratiof，the slenderness s，and the dimensionless stiffness matrix [K] .The Runge-Kutta and determinant search method were used to obtain the eigenvalues Ωiand eigenvectors that is mode shape.By calculating different configurations, the effects of slenderness s on the natural frequencies was much smaller than perfect supports.The effects of horizontal and vertical elastic supports on natural frequencies decreases with the frequencies of perfect supports increased .And the rotational elastic supports just obviously influence the fundamental frequency.
[1] Chidamparam P, Leissa A W. Vibrations Of Planar Curved Beams, Rings, And Arches[J]. Applied Mechanics Reviews, 1993, 46(9): 467–483.
[2] 项海帆. 拱结构的稳定与振动/高等结构力学丛书[M]. 人民交通出版社, 1991.
[3] Henrych J. The Dynamics Of Arches And Frames[M]. Elsevier Scientific Pub. Co., 1981.
[4] 钱七虎，孙乃光, 陈震元等. 拱型结构的自振频率计算及轴向变形对自振频率的影响[D]. 钱七虎院士论文选集, 1999.
[5] Karnovsky I A. Theory Of Arched Structures[M]. New York, Ny: Springer New York, 2012.
[6] Lee B K, Lee J Y, Choi K M等. Free Vibrations Of Arches With General Boundary Condition[J]. KSCE Journal Of Civil Engineering, 2002, 6(4): 469–474.
[7] 康婷, 白应生, 孙惠香. 水平弹性支撑圆拱的动力特性研究[J]. 力学与实践, 2013, 35(2): 50–55.
[8] Wung S. Vibration Of Hinged Circular Arches[D]. Rice University, 1967.
[9] 张相，黄东才. 结构振动力学[M]. 同济大学出版社, 1994.
[10] Al-Khafaji A W, Tooley J R. Numerical Methods In Engineering Practice[M]. Holt, Rinehart And Winston, 1986.
[11] Lee B K, Wilson J F. Free Vibrations Of Arches With Variable Curvature[J]. Journal Of Sound And Vibration, 1990, 136(1): 75–89.
[12] Lee B K, Lee T E, Ahn D S. Free Vibrations Of Arches With Inclusion Of Axial Extension, Shear Deformation And Rotatory Inertia In Cartesian Coordinates[J]. KSCE Journal Of Civil Engineering, 2004, 8(1): 43–48.
[13] Chidamparam P, Leissa A W. Influence Of Centerline Extensibility On The In-Plane Free Vibrations Of Loaded Circular Arches[J]. Journal Of Sound And Vibration, 1995, 183(5): 779–795.
[14] 金尼克. 拱的稳定性[M]. 建筑工程出版社, 1958.
[15] Fanning P J, Boothby T E, Roberts B J. Longitudinal And Transverse Effects In Masonry Arch Assessment[J]. Construction And Building Materials, 2001, 15(1): 51–60.
[16] 克拉夫, 彭津. 结构动力学[M]. 高等教育出版社, 2006.
