具有初始缺陷的扁球面网壳的混沌运动

Chaos motion of shallow reticulated spherical shells considering initial imperfection

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.

On the basis of the nonlinear dynamical foundational equations of three-way space truss,the large deflection equation and the nonlinear dynamic equation of the shallow spherical shells with initial imperfection were established by the method of quasi-shells.Dimensionless quantity of shells with uniform thickness was introduced and the foundational equations were simplified under the fixed boundary conditions.The large deflection of the shallow spherical shells was first solved.A nonlinear dynamic differential equation including the second and third order was then derived by the method of Galerkin.The critical conditions of chaos motion were given by solution of the Melnikov function.Using the digital simulation,the plane phase was plotted and it approved the existence of the chaos motion.It was found that the critical value of chaotic motion is smaller.