具有损伤扁球面网壳非线性稳定性

NONLINEAR STABILITY OF THE SHALLOW RETICULATED SPHERICAL SHELLS WITH DAMAGE

基于Lematire等效应变损伤原理,计及扁球面网壳各个杆件的损伤影响,根据薄壳非线性动力学理论推导出含有损伤扁球面网壳非线性动力学方程和协调方程,在固定夹紧边界条件下,用Galerkin方法得到一个含二次和三次非线性振动微分方程,并对具有损伤扁球面网壳的非线性自由振动方程求解.用Floquet指数法研究系统分叉问题给出了平衡点的状态.并通过数字仿真绘出了不同损伤状态下系统的分叉图和平衡点的相对位置图,发现损伤对系统的平衡点的状态影响较大.

Based on the theory of Lematire＇s equivalent strain of the damage, taking into account the damage of bars of the shallow reticulated spherical shell, and according to nonlinear dynamical theory of thin shells, the nonlinear dynamical equations and the consistency equation of the shallow reticulated shells with damage were obtained by quasi - shell method. Under the fixed and clamped boundary conditions, a nonlinear differential oscillation equation with quadric and cubic items was presented by the Galerkin method, and a nonlinear free oscillation equation of the shallow reticulated shells with damage was solved. Then the bifurcation of the system was discussed by Floquet exponent method, and the state of the equilibrium point was given. Lastly the bifurcation map and the relative position map of the equilibrium point were plotted by numerical emulation under the different damage state. It is founded that the damage of the bars of the shells greatly impacts on the state of the equilibrium point.