【作者】 王钢； 王新志； 韩明君； 丁雪兴；

【Author】 Wang Gang, Wang Xin-zhi, Han Ming-jun, Ding Xue-xing (Lan Zhou University of Technology,Lan Zhou 730050,PR China)

【机构】 兰州理工大学；

【摘要】 在圆形三向网架非线性动力学基本方程的基础上,用拟壳法给出了网底扁球面三向网壳的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,通过Galerkin作用得到了一个含二次、三次的非线性动力学方程。为求Melnikov函数,对一类非线性动力系统的自由振动方程进行了求解,且首次得到此类问题的准确解。在无激励情况下,讨论了稳定性问题。在外激励情况下,通过求Melnikov函数, 给出了可能发生混沌运动的条件。通过数字仿真绘出了平面相图,证实了混沌运动的存在。更多还原

【Abstract】 The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom based on the nonlinear dynamical foundational equations of circular reticulated structures with three-dimensional grids. Introduced another dimensionless quantities of shells with uniform thickness and simplify the foundational equations and the boundary conditions, a nonlinear differential equation containing the second and the third order is derived under the boundary conditions of fixed edges by using Galerkin method. In order to obtain the Melnikov function, the free oscillation equation of a kind of nonlinear dynamics system is solved, and then an exact solution to the problem is obtained for the first time as well. The problem of stability is discussed on the condition of none outer excitation, the conditions of that chaotic motion may appear are given by solution the Melnikov function under the condition of the outer excitation. Existence of the chaotic motion is approved by using digital simulation and draws the phase planes.更多还原