Nonlinear Dynamical Behavior of Shallow Cylindrical Reticulated Shells
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摘要: 用连续化法建立了正三角形网格的三向单层扁柱面网壳的非线性动力学方程和协调方程．在两对边简支条件下用分离变量函数法给出扁柱面网壳的横向位移．由协调方程求出张力，通过Galerkin作用得到了一个含二次、三次的非线性动力学微分方程．通过求Floquet指数讨论平衡点邻域的稳定性，用复变函数留数理论求出Melnikov函数，可得到该动力学系统发生混沌运动的临界条件．通过数值计算模拟和Poincaré映射也证明了混沌运动存在．Abstract: By using the method of quasi-shells,the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell were founded.By using the method of the separating variable function,the transverse displacement of the shallow cylindrical reticulated shells were given under the conditions of two edges simple support.The tensile force was solving from the compatible equations,a nonlinear dynamic differential equation containing the second and third order is derived by using the method of Galerkin.The stability near the equilibrium point was discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function.Existence of the chaotic motion of the single-layer shallow cylindrical reticulated shell is approved by using the digital simulation method and Poincar mapped.
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Key words:
- reticulated shells /
- method of quasi-shells /
- chaotic motion /
- critical condition
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