扁锥面单层网壳的非线性动力学特性

NON-LINEAR DYNAMIC CHARACTERSISTICS OF SINGLE-LAYER SHALLOW CONICAL LATTICE SHELLS

用拟壳法建立了正三角形网格三向扁锥面单层网壳的轴对称非线性动力学基本方程.通过分离变量函数法,用Galerkin法得到了一个含二次、三次的非线性微分方程.为了研究混沌运动,对一类非线性动力系统的自由振动方程进行了求解,给出了单层扁锥面网壳非线性自由振动微分方程的准确解.通过求Mel-nikov函数,给出了发生混沌运动的临界条件.数字仿真证实了混沌运动的存在.

By using the simulated shells method, this paper established the axisymmetrical non-linear dynamic equations for three-dimensional single-layer shallow conical lattice shells with equilateral triangle mesh. Through the separating variables function method, a quadric and cubic non-linear differential equation was obtained by using the Galerkin method. In order to study chaos movement,a kind of non-linear free vibration differential equation was solved, the accurate solution of the single-layer shallow conical cattice shells was obtained, and the critical condition was obtained by using the Melnikov function. Moreover, the numerical-graphic method also confirmed the existence of chaos.