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Structural Engineering and Mechanics Volume 40, Number 3, November10 2011 , pages 335-346 DOI: https://doi.org/10.12989/sem.2011.40.3.335 |
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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 |
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Yu Dong Chen, Chun Yan Pei and Su Huan Chen
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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. | ||
| Key Words | ||
| eigenvalue bifurcations; non-semi-simple eigenvalues; Hopf bifurcation; zero-order approximation solution; nonlinear systems | ||
| Address | ||
| Yu Dong Chen, Chun Yan Pei and Su Huan Chen: College of Mechanical Science and Engineering, Nanling Campus, Jilin University, ChangChun 130025, P.R. China | ||