Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems

陈衍茂,; 刘济科,

doi:10.1007/s10483-008-0207-x

Cited by 20 publications

(4 citation statements)

References 15 publications

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“…The bifurcation of an airfoil with both structural and aerodynamic nonlinearities in a supersonic flow field was investigated in [7] by using the center manifold theory and complex normal form method. Chen and Liu [8] studied the supercritical as well as subcritical Hopf bifurcation of an airfoil with cubic nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Liao

2013

Mathematical Problems in Engineering

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In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

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Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Liao

2013

Mathematical Problems in Engineering

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“…Most of the studies have focused on the numerical or analytical algorithms for solving the nonlinear aeroelastic equations, including the point transformation (PT) method [4] , the numerical continuation algorithm [5] , the center manifold method [6][7] , the perturbation incremental (PI) method [8] , the homotopy analysis method [9] , and the incremental harmonic balance method [10] . The describing function method was applied successfully to the flutter analyses of an aircraft for a variety of structural nonlinearities [11] .…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flow

Guo

Chen

2012

Appl. Math. Mech.-Engl. Ed.

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The nonlinear aeroelastic response of a two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flows is investigated. The second-order piston theory is used to analyze a double-wedge airfoil. Then, the fold bifurcation and the amplitude jump phenomenon are detected by the averaging method and the multi-variable Floquet theory. The analytical results are further verified by numerical simulations. Finally, the influence of the freeplay parameters on the aeroelastic response is analyzed in detail.

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“…Ding and Wang [11] also studied the flutter of an airfoil with cubic structural and aerodynamical nonlinearities by using the normal form method. The Hopf bifurcation of an airfoil flutter system with a cubic nonlinearity was investigated by Chen and Liu [12] by using the center manifold theory and complex normal form method. The results showed that for certain linear pitch stiffness, the Hopf bifurcation was supercritical as well as subcritical.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and chaos of an airfoil with cubic nonlinearity in incompressible flow

Chen

Zhou

Chen

2011

Sci. China Technol. Sci.

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Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (characterized by a negative eigenvalue, a simple zero eigenvalue and a pair of purely imaginary eigenvalues) for the bifurcation response equations is considered. With the aid of the normal form theory, the explicit expressions of the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. The stability of the bifurcation solutions is also investigated. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Si'lnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. Numerical simulations are also given, which confirm the analytical results. airfoil, bifurcation, chaotic motion Citation:Chen F Q, Zhou L Q, Chen Y S. Bifurcation and chaos of an airfoil with cubic nonlinearity in incompressible flow.

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Supercritical as well as subcritical Hopf bifurcation in nonlinear flutter systems

Cited by 20 publications

References 15 publications

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

Dynamic analysis of two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flow

Bifurcation and chaos of an airfoil with cubic nonlinearity in incompressible flow

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