THE STUDY ON CHAOTIC MOTION OF THE SHALLOW RETICULATED SPHERICAL SHELLS
扁球面网壳的混沌运动研究

By using the method of quasi-shells,the nonlinear dynamical equations are established for three- dimensional shallow spherical shells with circular bottom based on the nonlinear dynamical equations for circular reticulated structures with three-dimensional grids.The foundational equations and the boundary conditions are simplified by introducing dimensionless quantities,and a nonlinear differential equation of 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 the exact solution to the problem is obtained.The stability is discussed on the condition of no external excitation. The conditions for chaotic motion are given by solving for the Melnikov function under external excitations. Existence of the chaotic motion is proved by numerical simulation and the phase planes are plotted.