摘要
根据薄壳非线性动力学理论,由扁球薄壳大挠度基本方程,在周边固定夹紧的条件下,用修正迭代法求出二次近似解析解,把大挠度解作为扁球薄壳的初挠度处理,推导出扁球薄壳在大挠度下的非线性动力学基本方程。利用扁球面壳的非线性动力学变分方程和协调方程,在夹紧固定的边界条件下,用Galerkin方法得到一个含二次、三次项非线性受迫振动微分方程.通过求Melnikov函数,给出可能发生混沌运动的条件.通过数字仿真绘出平面相图,证实混沌运动的存在.
On the basis of nonlinear dynamical theory and according to control equations of flat spherical shallow shells under large deflection, the secondary approximate analytic solution was obtained by using a modified iteration method in the condition of fixedly clamped perimeter. Then, taking the large deflection solution as initial deflection of the flat spherical shells, the nonlinear dynamic control equations of the latter were derived in the case of large deflection. Employing nonlinear dynamic variational equation and compatible equation with boundary condition of clamped fixing, a nonlinear differential equation of forced vibration with second and third-order terms was obtained by using Galerkin approach. By means of finding the Melnikov function, a condition was given to the probable occurrence of chaotic motion. The existence of the latter was justified by the phase plane plotted with numerical simulation.
出处
《兰州理工大学学报》
CAS
北大核心
2007年第4期168-171,共4页
Journal of Lanzhou University of Technology
基金
甘肃省自然科学基金(3ZS042-B25-006)
关键词
非线性
大挠度
修正迭代法
混沌运动
nonlinearity
large deflection
modified iteration method
chaotic motion
