Structural Engineering and Mechanics

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Bifurcations of non-semi-simple eigenvalues and the zero-order approximations of responses at critical points of Hopf bifurcation in nonlinear systems

  • Chen, Yu Dong (College of Mechanical Science and Engineering, Nanling Campus, Jilin University) ;
  • Pei, Chun Yan (College of Mechanical Science and Engineering, Nanling Campus, Jilin University) ;
  • Chen, Su Huan (College of Mechanical Science and Engineering, Nanling Campus, Jilin University)
  • Received : 2010.08.13
  • Accepted : 2011.08.17
  • Published : 2011.11.10
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Abstract

This paper deals with the bifurcations of non-semi-simple eigenvalues at critical point of Hopf bifurcation to understand the dynamic behavior of the system. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method.

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References

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