Numerical studies of a non-linear aeroelastic system with plunging and pitching freeplays in supersonic/hypersonic regimes

Abbas, Laith K.; Chen, Q.; O'Donnell, K.; Valentine, Daniel T.; Marzocca, Pier

doi:10.1016/j.ast.2007.02.007

Cited by 33 publications

(28 citation statements)

References 18 publications

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“…The PTA is an inviscid unsteady aerodynamic theory, used extensively in the case of supersonic\hypersonic flow (M ∞ ≥ √ 2) and for moderate angles (|α| ≤ π/6). It provides a point-function relationship between the local pressure on the surface of the vehicle and the component of fluid velocity normal to the moving surface [22].…”

Section: Model Equationsmentioning

confidence: 99%

Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic\hypersonic flow

Guo

Chen

2011

Nonlinear Dyn

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In this paper, the Hopf bifurcations and limit cycle oscillations (LCOs) of an airfoil with cubic nonlinearity in supersonic\hypersonic flow are investigated. The harmonic balance method and multivariable Floquet theory are applied to analyze the LCOs of the airfoil. Four distinct cases of the LCOs response are detected in this system: (I) supercritical Hopf bifurcation, (II) a single subcritical Hopf bifurcation, (III) two subcritical Hopf bifurcations, and (IV) no Hopf bifurcation. Furthermore, the parameter variations domains separating the supercritical and subcritical Hopf bifurcations are presented using singularity theory.

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Section: Model Equationsmentioning

confidence: 99%

Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic\hypersonic flow

Guo

Chen

2011

Nonlinear Dyn

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“…L and M EA represent the unsteady aerodynamic lift and moment that can be obtained by the PTA [23] . The PTA is an inviscid unsteady aerodynamic theory, used extensively in the cases of supersonic/hypersonic flows (M ∞ √ 2) and moderate angles-of-attack (|α| π/6), which provides a point-function relationship between the local pressure on the surface of the vehicle and the component of the fluid velocity normal to the moving surface [24] .…”

Section: Model Equationsmentioning

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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“…Wong et al [10] have studied the nonlinear behavior of a two-dimensional aeroelastic system with freeplay models using a point transformation technique. Laith K. Abbas and Q. Chen et al [11] have studied the flutter and post-flutter of a two-dimensional double-wedge lifting surface with combined freeplay and cubic stiffness nonlinearities in both plunge and pitch degree-of-freedom, and the results have shown that the freeplay in the pitch DOF and cubic stiffness has significant effect on LCOs. P. Hémon and E. de Langre et al [12] presented experimental proof of a linear airfoil flutter from the view of the energy, and they have reported that even below the critical airspeed, large amplitude vibration may result from natural transient loading.…”

Section: Introductionmentioning

confidence: 96%

Random flutter of a 2-DOF nonlinear airfoil in pitch and plunge with freeplay in pitch

2009

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The two-degree-of-freedom (2-DOF) airfoil system with freeplay nonlinearity in pitch is investigated numerically. The relation between eigenvalues and flutter speed has been analyzed. The effect of parameters of the freeplay nonlinearity on the system responses is obtained. The probability density function (PDF) and phase plane of the deterministic system have been studied and the results show that the amplitude of limit cycle oscillation (LCO) grows with mean airspeeds increasing. Marginal PDFs, bidimensional PDFs, random bifurcation, and the largest Lyapunov exponent are used in investigation of the random system. The results show that, for low and intermediate level turbulences, the marginal PDFs of system exhibit different characters at different airspeed ranges. However, for high level turbulence the marginal PDFs are similar in the whole airspeed region. The bidimensional PDF has different shapes in low level turbulence at pre-and post-flutter speeds, but the PDF keeps similar shape in high level turbulence. The random bifurcation analysis indicates the P-bifurcation can happen at both pre-and post-flutter speeds but the D-bifurcation never occurs. Numerical simulations approve the results.

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Numerical studies of a non-linear aeroelastic system with plunging and pitching freeplays in supersonic/hypersonic regimes

Cited by 33 publications

References 18 publications

Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic\hypersonic flow

Supercritical and subcritical Hopf bifurcation and limit cycle oscillations of an airfoil with cubic nonlinearity in supersonic\hypersonic flow

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

Random flutter of a 2-DOF nonlinear airfoil in pitch and plunge with freeplay in pitch

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