矩形底面扁球面网壳的混沌与控制

Chaotic motion of reticulated shallow spherical shells with rectangular bottom and its control

对曲面为正三角形网格矩形底面扁球面单层网壳,用拟壳法建立非线性动力学方程,在固定夹紧的边界条件下,给出满足于边界条件的动态解.通过Galerkin作用得到该问题的非线性动力学方程,在受迫振动情况下用复变函数留数理论求出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.通过改变参数绘出的相轨图是封闭的,Poincare映射图具有有限点,抑制混沌运动发生.

The nonlinear dynamic equations for reticulated shallow spherical single-layer shells with equilateral triangular lattices and rectangular bottom was established by using the method of quasi-shells,and the dynamic solution fulfilling the boundary conditions was given under the conditions of clamped edges.The nonlinear dynamic equations for this problem were obtained by using Galerkin method,and then Melnikov function was found by using residue theorem of complex function with forced oscillation,and the condition of chaotic motion occurrence was given,also.Existence of chaotic motion was verified by using phase planes,Poincare maps and time history plots obtained with numeric simulation.The locus in phase plane was closed one and the number of point in Poincare maps was finite when the parameters were adjusted,so that the chaotic motion was suppressed.