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在圆形三向网架非线性动力学基本方程的基础上,用拟壳法给出了具有初始缺陷圆底扁球面网壳的大挠度方程和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.首先求出扁球面网壳的大挠度解,继之将大挠度解当作扁球面网壳的初始缺陷,通过Galerkin作用得到了一个含二次、三次的非线性动力学方程.通过求Melnikov函数,给出了具有初始缺陷的扁球面网壳系统可能发生混沌运动的临界条件.通过数字仿真绘出了平面相图,证实了混沌运动的存在.同时也发现考虑初始缺陷的扁球面系统固有频率增大了,从而发生混沌运动的临界载荷值减小了.
Based on the nonlinear dynamics fundamental equations of circular three-direction grids, a large deflection equation and a nonlinear basic dynamical equation for a circular flattened reticular dome with initial defects are given by using quasi-shell method. Under fixed boundary conditions , The dimensionless quantity of shell with different thickness is introduced and the basic equations and boundary conditions are dimensionless.Firstly, the solution of large-deflection shell of flat spherical shell is obtained, and then the solution of large deflection is taken as the initial of flat shell A nonlinear dynamic equation with second order and third order is obtained by Galerkin function. By solving the Melnikov function, the critical condition of possible chaos motion of the flat spherical reticulated shell system with initial defects is given. By numerical simulation The phase diagram confirms the existence of chaotic motion, and also finds that the natural frequency of the subspace system with initial defects increases and the critical load value of chaotic motion decreases.