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

WANG Xin-zhi; HAN Ming-jun; ZHAO Yan-ying; ZHAO Yong-gang

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Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(5): 586-590

WANG Xin-zhi, HAN Ming-jun, ZHAO Yan-ying, ZHAO Yong-gang. Nonlinear Dynamical Bifurcation and Chaotic Motion of a Shallow Conical Lattice Shell[J]. Applied Mathematics and Mechanics, 2006, 27(5): 586-590.

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

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

Received Date: 2004-04-16
Rev Recd Date: 2005-11-21
Publish Date: 2006-05-15

Abstract

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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References(10)

References

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