扁锥面网壳非线性动力分岔与混沌运动

王新志; 韩明君; 赵艳影; 赵永刚

扁锥面网壳非线性动力分岔与混沌运动

兰州理工大学理学院,兰州 730050

基金项目: 甘肃省自然科学基金资助项目(ZS042-B25-006)

详细信息

作者简介:
王新志(1940- ),男,河南淅川人,教授(联系人.Tel/Fax:+86-931-2975157;E-mail:Wangxz@lut.cn).

中图分类号: O343.5
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- 被引次数: 0
出版历程
- 收稿日期: 2004-04-16
- 修回日期: 2005-11-21
- 刊出日期: 2006-05-15

Nonlinear Dynamical Bifurcation and Chaotic Motion of a Shallow Conical Lattice Shell

School of Science, Lanzhou University of Technology, Lanzhou 730050, P. R. China

摘要

摘要: 对曲面为正三角形网格的3向扁锥面单层网壳，用拟壳法建立了轴对称非线性动力学方程．在几何非线性范围内给出了协调方程．网壳在周边固定条件下，通过Galerkin作用得到一个含2次、3次的非线性微分方程，通过求Floquet指数讨论了分岔问题．为了研究混沌运动，对一类非线性动力系统的自由振动方程进行了求解，继之给出了单层扁锥面网壳非线性自由振动微分方程的准确解，通过求Melnikov函数，给出了发生混沌的临界条件，通过数值仿真也证实了混沌运动的存在．
- 网壳 /
- 拟壳法 /
- 分岔 /
- 混沌
Abstract: The nonlinear dynamical equations of axle symmetry were established by using the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations were given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items was derived under the boundary conditions of fixed and clamped edges by using the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation to a kind of nonlinear dynamics system were solved. Then an exact solution to nonlinear free oscillation of the single-layer shallow conic lattice shell was found as well. The critical conditions of chaotic motion were obtained by solving Melnikov functions, some phase planes were drawn by using digital simulation and proved the existence of chaotic motion.
- lattice shell /
- the method of quasi-shell /
- bifurcation /
- chaotic motion

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参考文献(10)

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