Djamel Rezgui

Continuation and Bifurcation Analysis in Helicopter Aeroelastic Stability Problems

The dynamics of rotary wing systems are complex and typically feature highly nonlinear and often unsteady aerodynamics, as well as aeroelastic influences. In ongoing efforts to reduce noise and vibration, active devices such as trailing edge flaps on the rotor blades are being studied and these devices can introduce further nonlinearities. Therefore, it is important to be able to evaluate the stability of the overall system with a proper understanding of the global nonlinear behavior. Numerical continuation and bifurcation analysis is well suited to this need, and this paper presents evidence of the technique providing a deeper insight into the stability of helicopter rotor systems than the methods typically adopted in the industry. We first investigate the aeroelastic stability of rotor blades of a medium-sized helicopter in hover and the periodically forced forward flight condition, in both trimmed and untrimmed cases. Then, bifurcation analysis is used to predict the nonlinear stability of a single deg...

American Institue of Aeronautics and Astronautics

The dynamics of rotary wing systems is complex and typically features highly nonlinear and often unsteady aerodynamics as well as aeroelastic influences. In the helic opter industry and in ongoing efforts to reduce noise and vibration, the incorporation of active devices such as trailing edge flaps on the rotor blades is being studied. Such devices can introduce further nonlinearities. Therefore, it is important to be able to evaluate the stability of the overall system with sufficient insight into the global nonlinear behaviour. Numerical bifurcation analysis is well suited to this need, and this paper presents examples of the technique being used in efficiently evaluating the stability of helico pter rotor systems. The first example investigates the aeroelastic stability of rotor blades of a medium-sized helicopter in hover and the periodically forced forward flight condition, in both trimmed and untrimmed cases. In the second example, bifurcation analysis is used to predict the nonlinear stability of trailing edge flaps ‐ inco rporated in elastic blades ‐ over a range of design parameters, whereas the last example illustrates a case where bifurcation tools are used to study the nonlinear dynamics of a basic rotor model created in a commercial multi-body software.

A Combined Numerical/Experimental Continuation Approach Applied to Nonlinear Rotor Dynamics

Presented with complex systems exhibiting nonlinear behaviour, engineers in industry may face difficulties in understanding the system, both from a mathematical modeling perspective and also when trying to set up representative experiments. Here, a systematic approach combining numerical and experimental parameter continuation is applied to the investigation of complex nonlinear rotor behaviour. The aim is to show the benefits of co-ordinating numerical and physical tests in order to build a mathematical model that adequately captures the system dynamics. In this study the problem involves a dynamical system operating in a nonlinear periodic manner, with constraints on its states and parameters. The system is an autogyro rotor for which the approach generates a simple mathematical model yielding multiple possible autorotative conditions not previously identified in a systematic way; it also provides an explanation for unsafe operating scenarios.

On the nonlinear dynamics of a rotor in autorotation: a combined experimental and numerical approach

This article presents a systematic assessment of the use of numerical continuation and bifurcation techniques in investigating the nonlinear periodic behaviour of a teetering rotor operating in forward autorotation. The aim is to illustrate the potential of these tools in revealing complex blade dynamics, when used in combination (not necessarily at the same time) with physical testing. We show a simple procedure to promote understanding of an existing but not fully understood engineering instability problem, when uncertainties in the numerical modelling and constraints in the experimental testing are present. It is proposed that continuation and bifurcation methods can play a significant role in developing numerical and experimental techniques for studying the nonlinear dynamics not only for rotating blades but also for other engineering systems with uncertainties and constraints.

Experimental evaluation of numerical continuation and bifurcation methods applied to autogyro rotor blade aeromechanical stability

This paper presents a systematic assessment of the use of continuation and bifurcation techniques, in investigating the nonlinear periodic behaviour of rotor blades in forward autorotation. Our aim is to illustrate the potential of these tools in revealing complex blade dynamics, when used in combination (not necessarily in real time) with physical testing. We show a simple procedure to promote understanding of an existing engineering instability problem when uncertainties in the numerical modelling are present. It is proposed that continuation and bifurcation methods can play a significant role in developing numerical/experimental techniques for studying blade dynamics for both autorotating and powered rotors, which can be applied even at the preliminary design phase.Copyright

Nonlinear stability analysis of whirl flutter in a rotor-nacelle system

Whirl flutter is an aeroelastic instability that affects propellers/rotors and the surrounding airframe structure on which they are mounted. Whirl flutter analysis gets progressively more complicated with the addition of nonlinear effects. This paper investigates the impact of nonlinear pylon stiffness on the whirl flutter stability of a basic rotor-nacelle model, compared to a baseline linear stiffness version. The use of suitable nonlinear analysis techniques to address such a nonlinear model is also demonstrated. Three types of nonlinearity were investigated in this paper: cubic softening, cubic hardening and a combined cubic softening—quintic hardening case. The investigation was conducted through a combination of eigenvalue and bifurcation analyses, supplemented by time simulations, in order to fully capture the effects of nonlinear stiffness on the dynamic behaviour of the rotor-nacelle system. The results illustrate the coexistence of stable and unstable limit cycles and equilibria for a range of parameter values in the nonlinear cases, which are not found in the linear baseline model. These branches are connected by a number of different bifurcation types: fold, pitchfork, Hopf, homoclinic and heteroclinic. The results also demonstrate the importance of nonlinear whirl flutter models and analysis methods. Of particular interest are cases where the dynamics of the nacelle are unstable despite linear analysis predicting stable behaviour. A more complete stability envelope for the combined model was generated to take account of this phenomenon.

Testing of a Hinged Wingtip Device for Gust Loads Alleviation

Recent aircraft designs have considered higher-aspect-ratio wings to reduce induced drag for improved fuel efficiency; however, to remain compliant with airport gate requirements, folding wingtips ...

Proceedings of the ASME Design Engineering Technical Conference

This paper presents a systematic assessment of the use of continuation and bifurcation techniques, in investigating the nonlinear periodic behaviour of rotor blades in forward autorotation. Our aim is to illustrate the potential of these tools in revealing complex blade dynamics, when used in combination (not necessarily in real time) with physical testing. We show a simple procedure to promote understanding of an existing engineering instability problem when uncertainties in the numerical modelling are present. It is proposed that continuation and bifurcation methods can play a significant role in developing numerical/experimental techniques for studying blade dynamics for both autorotating and powered rotors, which can be applied even at the preliminary design phase.Copyright

7th International Conference on Multibody Systems, Nonlinear Dynamics and Control (IDETC), San Diego, CA, USA

This paper presents a systematic assessment of the use of continuation and bifurcation techniques, in investigating the nonlinear periodic behaviour of rotor blades in forward autorotation. Our aim is to illustrate the potential of these tools in revealing complex blade dynamics, when used in combination (not necessarily in real time) with physical testing. We show a simple procedure to promote understanding of an existing engineering instability problem when uncertainties in the numerical modelling are present. It is proposed that continuation and bifurcation methods can play a significant role in developing numerical/experimental techniques for studying blade dynamics for both autorotating and powered rotors, which can be applied even at the preliminary design phase.Copyright