具有初挠度扁柱面网壳的非线性动力学问题

根据薄壳非线性动力学理论和网格结构拟壳法,给出矩形底面扁柱面网壳的非线性混合边值问题, 在可移夹紧的边界条件下,求出扁柱面网壳的无量纲应力函数的解.利用扁柱面网壳的非线性动力学变分方程,通过Galerkin作用得到一个含二次和三次项的非线性动力学方程,在外激励情况下求Melnikov 函数,给出可能发生混沌运动的条件.通过数字仿真绘出的相轨图,Poincare映射图,时程图证实混沌运动的存在;给出频率受初挠度影响的特征曲线,结果表明频率随初挠度增大而增大,且随初挠度增大而非线性增强.

Nonlinear dynamic problem of reticulated shallow cylindric shells with the initial deformation

The nonlinear mixed boundary value problem of shallow reticulated cylindric shells with rectangular bottom was presented based on nonlinear dynamic theory of shallow shells and the method of quasi-shells of reticulated structures.The solution of dimensionless stress function of reticulated cylindric shells was found under the condition of clamped edges.By using nonlinear dynamic variational equation of the reticulated cylindric shells and Galerkin action,a nonlinear dynamic differential equation containing ...