Bifurcation analysis of airfoils in incompressible flow

Liu, J.-K.; Zhao, Lin

doi:10.1016/0022-460x(92)90407-o

Cited by 57 publications

(26 citation statements)

References 4 publications

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“…Subcritical as well as supercritical Hopf bifurcations are often encountered in different engineering applications, e.g., aeroelastic response of airfoils with structural nonlinearities [1,2], dynamics of ball joints [3], brake squeal [4]. Engineers are generally more concerned about subcritical (hard) bifurcations as a small perturbation around the equilibrium position can lead the system to large amplitude vibration states, which the structure may not tolerate [5].…”

Section: Introductionmentioning

confidence: 99%

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

2017

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The dynamical behavior of a single-degreeof-freedom system that experiences friction-induced vibrations is studied with particular interest on the possibility of the so-called hard effect of a subcritical Hopf bifurcation, using a velocity weakening-strengthening friction law. The bifurcation diagram of the system is numerically evaluated using as bifurcation parameter the velocity of the belt. Analytical results are provided using standard linear stability analysis and nonlinear stability analysis to large perturbations. The former permits to identify the lowest belt velocity (v lw ) at which the full sliding solution is stable, the latter allows to estimate a priori the highest belt velocity at which large amplitude stick-slip vibrations exist. Together the two boundaries [v lw , v up ] define the range where two equilibrium solutions coexist, i.e., a stable full sliding solution and a stable stick-slip limit cycle. The model is used to fit recent experimental observations.

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Section: Introductionmentioning

confidence: 99%

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

2017

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“…To the best of our knowledge, in model systems for turbo-machinery dynamics, snaking behaviour has never been investigated. Also systems from fluid-structure-interaction, may show weak non-linearity, Hopf bifurcation, and bi-stability, like models for aerofoil flap dynamics [20] [21][22] [23]. Similarly in friction induced vibrations the emergence of snaking could be well expected, with all the necessary ingredients like flutter instability and bi-stability already known to exist, cf.…”

Section: Introductionmentioning

confidence: 99%

Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

Papangelo

Grolet

Salles

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

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Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators are weakly nonlinear and subject to self-excitation and subcritical Hopf-bifurcations with some parameter ranges yielding bistability. When the oscillators are coupled to their neighbours, snaking bifurcations result, corresponding to localised vibration states. The snaking patterns do seem to be more complex than in previously studied continuous systems, comprising a plethora of isolated branches and also a large number of similar but not identical states, originating from the weak coupling of the phases of the individual oscillators.

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“…The high amplitude and frequencies associated with the flutter phenomena can cause catastrophic failure of the structure. The flutter of a two-dimensional wing with structural nonlinearity has been investigated in many works because of its simplicity and usefulness [1][2][3][4] . Yang and Zhao [5] have a systematic investigation by the harmonic balance method.…”

Section: Introductionmentioning

confidence: 99%

Chaotic motions and limit cycle flutter of two-dimensional wing in supersonic flow

Zheng

Yang

2008

Acta Mech. Solida Sin.

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Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos are very narrow.

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Bifurcation analysis of airfoils in incompressible flow

Cited by 57 publications

References 4 publications

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry

Chaotic motions and limit cycle flutter of two-dimensional wing in supersonic flow

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