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。并将扁球面网壳的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。并通过数字仿真绘出了平面相图,证实了混沌运动的存在并且可以通过改变参数来抑制系统混沌运动的发生。同时也发现了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 fendamented equations, the big deflection equation and the nonlinear dynamic equation of the shallow spherical shells were established by the method of quasi-shells. Dimensionless quantity of shells with uniform thickness was introduced and used to simplify the fendamental equations and the boundary conditions under the fixed boundary conditions. The static big deflection was taken as the initial imperfect assumption of the system and a nonlinear dynamic differential equation including the second and third order terms was derived by the method of Galerkin. The critical conditions of the chaos motion were given by solving the Melnikov function. Using the digital simulation the plane phase diagram was plotted and the existence of the chaotic motion is approved. It is also approved that the chaos could be controlled by changing parameters. It is found that the first natural frequency of shallow reticulated spherical shells considering initial imperfect becomes higher and the critical value of chaotic motion becomes smaller.
出处
《振动与冲击》
EI
CSCD
北大核心
2009年第6期6-7,41,共3页
Journal of Vibration and Shock
基金
国家自然科学基金项目(59978038)资助
关键词
初始缺陷
拟壳法
混沌
扁球面网壳
非线性
稳定性
initial imperfect
quasi-shells
chaos motion
shallow reticulated spherical shells
non-linear
stability
