扁球面网壳在动静荷载作用下的非线性稳定性

Non-linear stability of the shallow reticulated spherical shell with stationary load and dynamic load

根据薄壳非线性动力学理论和拟壳法的思想,给出了扁球面网壳在动、静荷载协同作用下的非线性动力学控制方程.然后利用扁球面网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,通过Galerkin作用得到一个含二次和三次的非线性动力学微分方程.用Floquet指数方法研究了系统的分岔问题,讨论了平衡点(奇点)邻域的稳定性问题.指出了系统在纯动态作用和在动静荷载协同作用下其平衡位置的变化情况.

According to the nonlinear dynamical theory of plate-shell and ideology of continuous quasi-shell method, nonlinear dynamical governing equations under the load of both dynamic and static were given. Then using nonlinear dynamical variation equations and compatible equations of the shallow reticulated conical shell, a nonlinear differential equation with quadric and cubic items was obtained by the Galerkin method under the fixed edges boundary condition. The problem of statistic at the equilibrium point of the system was discussed by exponent Floquet. And the movement of the equilibrium point of the system under the dynamic load and the load of both dynamic and static was indicated.