• Steel and Composite Structures
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• v.6 no.5
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• pp.401-415
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• 2006

Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

• Structural Engineering and Mechanics
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• v.40 no.3
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• pp.335-346
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• 2011

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.

• Journal of Power Electronics
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• v.14 no.6
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• pp.1208-1216
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• 2014

Mismatch between switching frequency and circuit parameters often occurs in industrial applications, which would lead to instability phenomena. The bifurcation behavior of $V^2$ controlled buck converter is investigated as the pulse width modulation period is varied. Nonlinear behavior is analyzed based on the monodromy matrix of the system. We observed that the stable period-1 orbit was first transformed to the period-2 bifurcation, which subsequently changed to chaos. The mechanism of the series of period-2 bifurcations shows that the characteristic eigenvalue of the monodromy matrix passes through the unit circle along the negative real axis. Resonant parametric perturbation technique has been applied to prevent the onset of instability. Meanwhile, the extended stability region of the converter is obtained. Simulation and experimental prototypes are built, and the corresponding results verify the theoretical analysis.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.61-69
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• 1997

In this paper, we study the dynamics of a two-parameter unfolding system $\chi$' = y, y' = $\beta$y＋$\alpha$f($\chi\alpha\pm\chiy$＋yg($\chi$), where f($\chi$,$\alpha$) is a second order polynomial in $\chi$ and g($\chi$) is strictly nonlinear in $\chi$. We show that the higher order term yg($\chi$) in the system does not change qulitative structure of the Hopf bifurcations near the fixed points for small $\alpha$ and $\beta$ if the nontrivial fixed point approaches to the origin as $\alpha$ approaches zero.