Multi-pulse orbits and chaotic dynamics in a nonlinear forced dynamics of suspended cables
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- 作者：Yugao Huangfu (12) huangfuyugao@163.com
Fangqi Chen (13) - 关键词：Suspended cables – ; Global bifurcation – ; Energy phase method – ; Multi ; pulse orbit
- 刊名：Archive of Applied Mechanics (Ingenieur Archiv)
- 出版年：2011
- 出版时间：September 2011
- 年：2011
- 卷：81
- 期：9
- 页码：1231-1252
- 全文大小：1.0 MB
- 参考文献：1. Tong X., Tabarrok B.: Melnikovsmethod for rigid bodies subject to small perturbation torques. Arch. Appl. Mech. 66, 215–230 (1996)
2. Ravindra B., Zhu W.D.: Low-dimensional chaotic response of axially accelerating continuum in the supercritical regime. Arch. Appl. Mech. 68, 195–205 (1998)
3. Wiggins S.: Global Bifurcations and Chaos. Springer, New York (1988)
4. Kovačič G., Wiggins S.: Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation. Phys. D 57, 185–225 (1992)
5. Kaper T.J., Kovačič G.: Multi-bump orbits homoclinic to resonance bands. Trans. Am. Math. Soc. 348, 3835–3887 (1996)
6. Camassa R., Kovačič G., Tin S.K.: A Melnikov method for homoclinic orbits with many pulse. Arch. Ration. Mech. Anal. 143, 105–193 (1998)
7. Haller G., Wiggins S.: Orbits homoclinic to resonances: the Hamiltonian case. Phys. D 66, 298–346 (1993)
8. Haller G., Wiggins S.: N-pulse homoclinic orbits in perturbations of resonant Hamiltonian system. Arch. Ration. Mech. Anal. 130, 25–101 (1995)
9. Haller G., Wiggins S.: Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schr枚dinger equation. Phys. D 85, 311–347 (1995)
10. Mcdonald R.J., Sri Namachchivaya N.: Pipes conveying pulsating fluid near a 0:1 resonance: global bifurcations. J. Fluids Struct. 21, 665–687 (2005)
11. Feng Z.C., Wiggins S.: On the existence of chaos in a class of two-degree-of-freedom, damped parametrically forced mechanical systems with broken O(2) symmetry. ZAMP 44, 201–248 (1993)
12. Feng Z.C., Sethna PR.: Global bifurcation in motions of parametricaliy excited thin plates. Nonlinear Dyn. 4, 398–408 (1993)
13. Feng Z.C., Liew K.M.: Global bifurcations in parametrically excited systems with zero-to-one internal resonance. Nonlinear Dyn. 21, 249–263 (2000)
14. Wei Z., Minghui Y.: Multi-pulse orbits and chaotic dynamics in motion of parametrically excited viscoelastic moving belt. Chaos Solitons Fractals 28, 42–66 (2006)
15. Wei Z., Wang F.X., Minghui Y.: Global bifurcations and chaotic dynamics in nonlinear nonplanar oscillations of a parametrically excited cantilever beam. Nonlinear Dyn. 40, 251–279 (2005)
16. Narakorn S., Giuseppe R.: The effects of kinematic condensation on internally resonant forced vibrations of shallow horizontal cables. Int. J. Nonlinear Mech. 42, 180–195 (2007)
17. Narakorn S., Giuseppe R.: Nonlinear longitudinal/transversal modal interactions in highly extensible suspended cables. J. Sound Vib. 310, 230–242 (2008)
18. Narakorn S., Giuseppe R.: Space-time numerical simulation and validation of analytical predictons for nonlinear forced dynamics of suspended cables. J. Sound Vib. 310, 230–242 (2008) - 作者单位：1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, People鈥檚 Republic of China2. College of Mathematics and Information Science, Henan Polytechnic University, 454000 Jiaozuo, People鈥檚 Republic of China3. Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, 300072 Tianjin, People鈥檚 Republic of China
- 刊物类别：Engineering
- 刊物主题：Theoretical and Applied Mechanics
Mechanics
Complexity
Fluids
Thermodynamics
Systems and Information Theory in Engineering - 出版者：Springer Berlin / Heidelberg
- ISSN：1432-0681
文摘
The global bifurcations in mode of a nonlinear forced dynamics of suspended cables are investigated with the case of the 1:1 internal resonance. After determining the equations of motion in a suitable form, the energy phase method proposed by Haller and Wiggins is employed to show the existence of the Silnikov-type multi-pulse orbits homoclinic to certain invariant sets for the two cases of Hamiltonian and dissipative perturbation. Furthermore, some complex chaos behaviors are revealed for this class of systems.