单层扁锥面网壳非线性动力稳定性分析

用拟壳法建立了正三角形网格的三向扁锥面单层网壳的非线性动力学微分方程。在周边固定条件下,用分离变量函数法给出网壳的横向位移。由协调方程求出张力,通过Galerkin作用得到了一个含二次、三次的非线性微分方程,在不考虑外激励情况下,此系统有三个平衡点。通过求Floquet指数讨论了零平衡点邻域的稳定性问题。为了研究系统的混沌运动,在给定的初始条件下,对此动力系统的非线性自由振动方程进行了求解,首次得到了带平方和立方非线性系统的准确解,使得求Melnikov函数成为可能。用复变函数中的留数理论求出了Melnikov函数,得到了发生混沌的临界条件,通过数值仿真和Poincare映射也证实了混沌运动的存在。

NON-LINEAR DYNAMIC STABILITY ANALYSIS OF SINGLE-LAYER CONICAL LATTICE SHELLS

Using the method of simulated shell, non-linear dynamic differential equation of three-dimensional single-layer shallow lattice shell with equilateral triangle mesh is established. The lateral displacement of lattice shell is obtained by separation of variables for fixed boundary condition. The stretching force is obtained from the compatibility equation. A non-linear differential equation with quadratic and cubic terms is established by Galerkin method. The system has three equilibrium points on the condition that external excitation is ignored. Stability close to the null equilibrium point is discussed by the Floquet exponent. In order to study the chaos motion, non-linear free vibration equation of this dynamic system is solved with the given initial conditions. An accurate solution of the non-linear free vibration system is obtained. This makes Melnikov founction obtainable. Melnikov founction is obtained by theory of residuals, and the critical condition is also obtained. Numerial-graphic method and Poincare map confirm the existence of chaos.