扁球面网壳的混沌运动研究  

THE STUDY ON CHAOTIC MOTION OF THE SHALLOW RETICULATED SPHERICAL SHELLS

作　　者：邱平[1] 韩明君[1] 王钢[1] 王新志[1] 

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《力学与实践》2006年第5期39-42,共4页Mechanics in Engineering

基　　金：甘肃省自然科学基金项目(3zso42-B25-006)资助.

摘　　要：在圆形三向网架非线性动力学基本方程的基础上,用拟壳法给出了圆底扁球面三向网壳的非线性动力学基本方程．在固定边界条件下,引入了异于等厚度壳的无量纲量,对基本方程和边界条件进行无量纲化,通过Galerkin作用得到了一个含二次、三次的非线性动力学方程．为求Melnikov函数,对一类非线性动力系统的自由振动方程进行了求解,得到了此类问题的准确解．在无激励情况下,讨论了稳定性问题．在外激励情况下,通过求Melnikov函数,给出了可能发生混沌运动的条件．通过数字仿真绘出了平面相图,证实了混沌运动的存在．By using the method of quasi-shells, the nonlinear dynamical equations are established for threedimensional shallow spherical shells with circular bottom based on the nonlinear dynamical equations for circular reticulated structures with three-dimensional grids. The foundational equations and the boundary conditions are simplified by introducing dimensionless quantities, and a nonlinear differential equation of the third order is derived under the boundary conditions of fixed edges by using Galerkin method. In order to obtain the Melnikov function, the free oscillation equation of a kind of nonlinear dynamics system is solved, and then the exact solution to the problem is obtained. The stability is discussed on the condition of no external excitation. The conditions for chaotic motion are given by solving for the Melnikov function under external excitations. Existence of the chaotic motion is proved by numerical simulation and the phase planes are plotted.

关 键 词：拟壳法 混沌 网壳 准确解 

分 类 号：O415.5[理学—理论物理]