Prediction and suppression of chaotic instability in brake squeal

Meehan, Paul A.

doi:10.1007/s11071-021-06992-1

Cited by 4 publications

(8 citation statements)

References 43 publications

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“…0 ∆𝑝 1 assuming the elastic centre and centre of pressure are aft of the centre of gravity and elastic centre, respectively. The closed form solution (26) predicts that the classical critical flutter speed increases with increases in rotational inertia, spacing between uncoupled plunging (bending) and pitching (torsional) natural frequencies and decreases in air density. Added damping will tend to increase the critical flutter speed as well.…”

Section: Stiffness Mode Coupled Fluttermentioning

confidence: 99%

“…where 𝑊 , is the critical flutter speed obtained in closed form as (26) under no damping. Equation ( 28) is a conservative criterion as it has accounted for continuous averaging of the local trajectory expansion in phase space and it is only necessary as it only measures sensitivity to initial conditions.…”

Section: Predicting Chaotic Flutter In a Wind Turbinementioning

confidence: 99%

“…shows the critical flutter speed (116.5 m/s) using (26) and [3] under the same conditions. Assumed constant nominal vibration frequency as wind speed changes.…”

Section: Figure 5 Local Stability Solutions Of the Optimised Wind Tur...mentioning

confidence: 99%

“…The critical flutter speed was investigated further by determining how it varies along the wind turbine blade (26) in Figure 6 along with the local wind speed. In particular, Figure 6 predicts flutter will occur when the local wind speed exceeds the critical flutter speed in the shaded region.…”

Section: Figure 5 Local Stability Solutions Of the Optimised Wind Tur...mentioning

confidence: 99%

“…Note, alternatively the damping ratio will be lowered if the damping is held constant as blade length increases, causing chaotic flutter to more likely occur.  Wind turbine blade flutter and chaos can be suppressed by changes in modal mass or stiffness by separating (detuning) the plunging and pitching natural frequencies or lowering the modal mass according to (26), to increase the critical flutter speed due to stiffness mode coupling.  A reasonable increase in the pitch modal damping (>+1x) damps out any chaotic overlapping harmonic resonances from parametric excitation, caused by the bilinear lift curve.…”

Section: Chaotic Flutter Suppressionmentioning

confidence: 99%

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Prediction and Suppression of Chaotic Flutter in Wind Turbines

Meehan

2023

Preprint

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Chaotic motion in a fluttering wind turbine blade is investigated using an efficient analytical predictive model that is then used to suppress the phenomenon. Flutter is a dynamic instability of an elastic structure in a fluid, such as an airfoil section of a wind turbine blade. It is presently modelled using generalised two degree of freedom coupled modes of a blade airfoil section (pitch and plunge) combined with local unsteady aerodynamics, based on flutter derivatives and a continuous bilinear lift curve under damping. The mode coupling causes instability and limit cycle behaviour due to a Hopf bifurcation that may lead to period doubling and chaotic behaviour after the critical flutter speed. New closed form conservative analytical conditions for blade flutter chaos are identified and discussed for the wind turbine section taking into account the blade geometry and optimal design of the wind turbine. These predictions are numerically verified for a range of conditions including stall slope and damping. The results confirm that blade flutter chaos can occur due to nonlinearities in the aerodynamics i.e. due to a bilinear lift law. This phenomenon is then suppressed to unrealistically high wind speeds and/or eliminated by quantified variation of system parameters using the predictive model. The results show that small changes in tip speed ratio (-15%) and stall slope factor (-17%) can eliminate or suppress chaotic flutter while in general larger changes in dynamic parameters (ie mass, stiffness, damping) are required to achieve the same, by detuning the coupled plunge and pitch natural frequencies or damping out overlapping parametric resonances. General insight is also provided into the occurrence and suppression of airfoil flutter chaos in aeroelastic structures like wind turbines.

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Section: Stiffness Mode Coupled Fluttermentioning

confidence: 99%

Section: Predicting Chaotic Flutter In a Wind Turbinementioning

confidence: 99%

“…shows the critical flutter speed (116.5 m/s) using (26) and [3] under the same conditions. Assumed constant nominal vibration frequency as wind speed changes.…”

Section: Figure 5 Local Stability Solutions Of the Optimised Wind Tur...mentioning

confidence: 99%

Section: Figure 5 Local Stability Solutions Of the Optimised Wind Tur...mentioning

confidence: 99%

Section: Chaotic Flutter Suppressionmentioning

confidence: 99%

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Prediction and Suppression of Chaotic Flutter in Wind Turbines

Meehan

2023

Preprint

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Prediction and suppression of chaos following flutter in wind turbines

Meehan

2023

Nonlinear Dyn

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Chaotic motion in a fluttering wind turbine blade is investigated by the development of an efficient analytical predictive model that is then used to suppress the phenomenon. Flutter is a dynamic instability of an elastic structure in a fluid, such as an airfoil section of a wind turbine blade. It is presently modelled using generalised two degree of freedom coupled modes of a blade airfoil section (pitch and plunge) combined with local unsteady aerodynamics, based on flutter derivatives and a continuous bilinear lift curve under damping. The mode coupling causes instability and limit cycle flutter due to a Hopf bifurcation. Following the critical flutter speed, the response can transition to chaos through successive other bifurcations like period doubling. New closed-form conservative analytical conditions for chaos following blade flutter are identified and discussed for the wind turbine section taking into account the blade geometry and optimal design of the wind turbine. These predictions are numerically verified for a range of conditions including stall slope and damping. The results confirm that chaos following blade flutter can occur due to nonlinearities in the aerodynamics, i.e. due to a bilinear lift law. This phenomenon is then suppressed to unrealistically high wind speeds and/or eliminated by quantified variation of system parameters using the predictive model. The results show that small changes in tip speed ratio (−15%), and stall slope factor (−17%) can eliminate or suppress chaos following flutter, while, in general, larger magnitude changes in dynamic parameters (i.e. mass, inertia > 81%, stiffness > 97%, damping > 100%) are required to achieve the same, by detuning the coupled plunge and pitch natural frequencies or damping out overlapping parametric resonances. These results also highlight that the analytical predictions can remarkably be generalized to any parameter set and provide almost instantaneous calculations representing many thousands of numerical simulations from many bifurcation diagrams (computational acceleration factor of 107 times). General insight is also provided into the occurrence and suppression of airfoil chaos following flutter in aeroelastic structures like wind turbines.

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The role of dynamic friction in the appearance of periodic oscillations in mechanical systems

González-Carbajal,

García-Vallejo,

Domínguez

et al. 2024

Nonlinear Dyn

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This article investigates the appearance of periodic mechanical oscillations associated with the transition between static and dynamic friction regimes. The study employs a mechanical system with one degree of freedom and a friction model recently proposed by Brown and McPhee, whose continuity and differentiability properties make it particularly appropriate for an analytical treatment of the equations. A bifurcation study of the system, including stability analysis, transformation to normal form and numerical continuation techniques, reveals that stable periodic orbits can be created either by a supercritical Hopf bifurcation or by a saddle-node bifurcation of limit cycles. The influence of all system parameters on the appearance of periodic oscillations is investigated in detail. In particular, the effect of the friction model parameters (static-to-dynamic friction ratio and transition speed between the static and dynamic regimes) on the bifurcation behavior of the system is addressed.

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Prediction and suppression of chaotic instability in brake squeal

Cited by 4 publications

References 43 publications

Prediction and Suppression of Chaotic Flutter in Wind Turbines

Prediction and Suppression of Chaotic Flutter in Wind Turbines

Prediction and suppression of chaos following flutter in wind turbines

The role of dynamic friction in the appearance of periodic oscillations in mechanical systems

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