Based on the theory of Lematire's equivalent strain of damage and in consideration of the damage of bars in a shallow reticulated spherical shell, nonlinear dynamical equations of the deteriorated shallow reticulated spherical shell were put forward by using the quasi-shell method. The method of perturbation-variation was presented, in which the maximal amplitude at the center of the shell was taken as the perturbation parameter. Then the nonlinear vibration equation of the system under fixed and clamped boundary conditions was solved by perturbation-variation method and the corresponding eigen-relation was obtained. Further, Galerkin method was utilized to derive a differential vibration equation, including the 2nd and 3rd order nonlinear terms and an accurate free vibration solution of the deteriorated shell was achieved. Then, the theoretical critical condition of chaos motion was given by using Melnikov function method and the chaos motions of the shell under nonlinear forced vibration were simulated numerically. It is found that the damage bars make the system occur more easily chaos motion.%基于Lematire等效应变损伤理论,计及扁球面网壳各个杆件的损伤影响,应用拟壳法导出了具有损伤的扁球面网壳的动力学非线性控制方程.提出了以中心最大振幅为摄动参数的摄动-变分法的求解方法,对动力非线性控制方程进行了求解,得出了相应的物理量的解析式.据此进行数值分析,得出了相应的特征关系.并用Galerkin方法导出了一个含二次和三次非线性振动微分方程并求解了具有损伤扁球面网壳的的非线性动力学的自由振动方程,给出了准确解.而后利用Melnikov函数法,从理论上给出了考虑损伤的系统发生混沌运动的临界条件,并通过计算机数字仿真证实了考虑损伤的扁球面网壳在非线性强迫振动时存在混沌运动,同时发现损伤使得系统更易发生混沌运动.
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