Nonlinear Dynamical Bifurcation and Chaotic Motion of a Shallow Conical Lattice Shell
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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．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.
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Key words:
- lattice shell /
- the method of quasi-shell /
- bifurcation /
- chaotic motion
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