圆形三向网架非线性动力稳定性分析  

Nonlinear Dynamical Stability Analysis of the Circular Three-Dimensional Frame

作　　者：王新志[1] 王钢[1] 赵艳影[1] 叶开沅[2] 

机构地区：[1]兰州理工大学理学院,兰州730050 [2]兰州大学物理学院,兰州730000

出　　处：《应用数学和力学》2004年第4期331-336,共6页Applied Mathematics and Mechanics

基　　金：甘肃省自然科学基金资助项目(ZS021_A25_007_Z)

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。The three-dimensional frame is simplified into flat plate by the method of quasi-plate.The nonlinear relationships between the surface strain and the midst plane displacement are established.According to the thin plate nonlinear dynamical theory,the nonlinear dynamical equations of three^dimensional frame in the orthogonal coordinates system are obtained.Then the equations 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 boundary 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-dimensional frame are studied 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 artificial method.

关 键 词：三向网架 拟板法 分岔 混沌 

分 类 号：O343.5[理学—固体力学] O326[理学—力学]