Nonlinear Dynamical Stability Analysis of the Circular Three-Dimensional Frame
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摘要: 用拟板法将网架简化为平板,给出表层应变与中面位移的非线性关系.根据薄板的非线性动力学理论,建立了在直角坐标系中三向网架的非线性动力学方程,又将此方程转化为极坐标系轴对称非线性动力学方程.在周边固定条件下,引入异于等厚度板的无量纲量,对基本方程无量纲化.利用Galerkin法得到一个三次非线性振动方程,在无外激励情况下,讨论了稳定性与分岔问题.在外激励情况下,用Melnikov方法研究了圆形三向网架可能发生的混沌运动.通过数字仿真绘出了发生混沌的相平面图.Abstract: The three dimensional frame is simplified into flat plate by the method of quasi-plate. The nonlinear relationships between the surface strain and the ntidst plane displacement are established According to the thin plate nonlinex dynantical theory,the nonlinear dynantical equations of threedimensional frame in the orthogonal coordinates system are obtained Then the equatiorn are translated into the axial symmetry nonlinear dynamical equations in the polar coordinates system. Some dimensionless quantities different from the plate of uniform thickness are introduced under the boundxy conditions of fixed edges,then these fundamental equations are simplified with these dimensionless quantities. A cubic nonlinear vibration equation is obtained with the method of Galerkin. The stability and bifurcation of the circular three-dimernional frame are steadied under the condition of without outer motivation. The contingent chaotic vibration of the three-dimensional frame is studied with the method of Melnikov. Some phase figures of contingent chaotic vibration are plotted with digital artifivial method.
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Key words:
- three-dimensional frame /
- quasi-plate method /
- bifurcation /
- chaos
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[1] 聂国华,刘人怀.矩形网格扁壳的非线性特征关系[J].土木工程学报,1995,28(1):12—21. [2] 肖潭,刘人怀.斜放四角锥扁网壳的非线性弯曲理论[J].应用数学和力学,2001,22(7):666—672. [3] 朱忠义,董石麟,高博青.折板网壳的几何非线性分析[J].工业建筑,2001,31(2):51—59. [4] 董石麟,张志宏,李元齐.空间网格结构几何非线性有限元分析方法的研究[J].计算力学学报,2002,19(3):365—368. [5] 聂国华.矩形网格扁壳结构的非线性振动[J].应用数学和力学,1994,15(6):495—503. [6] 高博青,董石麟. 折板式网壳结构的动力性能分析[J].建筑结构学报,2002,23(1):53—57. [7] 韩强,张善元,杨桂通.一类非线性动力系统混沌运动的研究[J].应用数学和力学,1999,20(8):776—782. [8] Moon F C,Shaw S W.Chsotic vibration of a beam with nonlinear boundary conditions [J].Nonlinear Mechanics,1983,18(6):465—477. doi: 10.1016/0020-7462(83)90033-1 [9] 赵艳影,王新志,赵永刚,等.圆形三向网架的非线性弯曲分析[J].兰州理工大学学报,2003,29(3):143—145.
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