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See detailNonlinear modal analysis of a full-scale aircraft
Kerschen, Gaëtan ULg; Peeters; Golinval, Jean-Claude ULg et al

in Journal of Aircraft (2013), 50

Nonlinear normal modes (NNMs), which are defined as a nonlinearextension of the concept of linear normal modes, are a rigorous tool for nonlinear modal analysis. The objective of this paper is to ... [more ▼]

Nonlinear normal modes (NNMs), which are defined as a nonlinearextension of the concept of linear normal modes, are a rigorous tool for nonlinear modal analysis. The objective of this paper is to demonstrate that the computation of NNMs and of their oscillation frequencies can now be achieved for complex, real-world aerospace structures. The application considered in this study is the airframe of the Morane-Saulnier Paris aircraft. Ground vibration tests of this aircraft exhibited softening nonlinearities in the connection between the external fuel tanks and the wing tips. The NNMs of this aircraft are computed from a reduced-order nonlinear finite element model using a numerical algorithm combining shooting and pseudo-arclength continuation. Several NNMs, involving, e.g., wing bending, wing torsion and tail bending, are presented, which highlights that the aircraft can exhibit very interesting nonlinear phenomena. Specifically, it is shown that modes with distinct linear frequencies can interact and generate additional nonlinear modes with no linear counterpart. [less ▲]

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See detailShooting-Based Complete Bifurcation Prediction for Aeroelastic Systems with Freeplay
Dimitriadis, Grigorios ULg

in Journal of Aircraft (2011), 48(6), 1864-1877

In recent years there have been several applications of numerical continuation approaches to aeroelastic systems with freeplay. While some of these have been successful, the general application of the ... [more ▼]

In recent years there have been several applications of numerical continuation approaches to aeroelastic systems with freeplay. While some of these have been successful, the general application of the method to such systems remains problematic. Numerical continuation can fail in the presence of complex bifurcations, numerous nearby periodic solution branches and other factors. In this paper, a three-part procedure for applying numerical continuation to aeroelastic systems with freeplay is proposed, designed to ensure that the complete periodic behavior is identified, even for systems with very complex bifurcation diagrams. First, the equivalent linearization approach is used to determine approximations to the periodic solutions of the nonlinear system. Then, a shooting-based technique is applied separately to each linearized approximation in order to pinpoint the nearest exact periodic solution. This process results in a cloud of periodic solutions, representing points on all the solution branches and sub-branches. Finally, a branch-following shooting procedure is applied to this cloud of points in order to obtain a complete description of every branch of periodic solutions. The methodology is applied to a simple aeroelastic system with three degrees of freedom and freeplay in the control surface. This system has been often studied but never fully characterised. It is shown that the proposed method succeeds in describing the complete bifurcation behaviour of the system and explaining its limit cycle response. [less ▲]

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See detailIdentification of a Nonlinear Wing Structure Using an Extended Modal Model
Platten, M. F.; Wright, J. R.; Cooper, J. E. et al

in Journal of Aircraft (2009), 46(5), 1614-1626

The nonlinear resonant decay method identifies a nonlinear dynamic system using a model based in linear modal space comprising the underlying linear system and a small number of additional terms that ... [more ▼]

The nonlinear resonant decay method identifies a nonlinear dynamic system using a model based in linear modal space comprising the underlying linear system and a small number of additional terms that represent the nonlinear behavior. In this work, the method is applied to an aircraftlike wing/store/pylon experimental structure that consists of a rectangular wing with two stores suspended beneath it by means of nonlinear pylons with a nominally hardening characteristic in the store rotation degree of freedom. The nonlinear resonant decay method is applied to the system using multishaker excitation. The resulting identified mathematical model features five modes, two of which are strongly nonlinear, one is mildly nonlinear, and two are completely linear. The restoring force surfaces obtained from the mathematical model are in close agreement with those measured from the system. This experimental application of the nonlinear resonant decay method indicates that the method could be suitable for the identification of nonlinear models of aircraft in ground vibration testing. [less ▲]

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See detailBifurcation analysis of aircraft with structural nonlinearity and freeplay using numerical continuation
Dimitriadis, Grigorios ULg

in Journal of Aircraft (2008), 45(3), 893-905

In recent years the aeroelastic research community has carried out substantial work on the characterization and prediction of nonlinear aeroelastic phenomena. Of particular interest is the calculation of ... [more ▼]

In recent years the aeroelastic research community has carried out substantial work on the characterization and prediction of nonlinear aeroelastic phenomena. Of particular interest is the calculation of Limit Cycle Oscillations (LCO), which cannot be accomplished using traditional linear methods. In this paper, the prediction of the bifurcation and post-bifurcation behavior of nonlinear subsonic aircraft is carried out using Numerical Continuation. The analysis does not make use of continuation packages such as AUTO or MatCont. Two different continuation techniques are detailed, specifically adapted for realistic aeroelastic models. The approaches are demonstrated on model of a simple pitch plunge airfoil with cubic stiffness and an aeroelastic model of a transport aircraft with two different types of nonlinearity in the control surface. It is shown that one of the techniques yields highly accurate predictions for LCO amplitudes and periods while the second method trades off some accuracy for computational efficiency. [less ▲]

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See detailContinuation of Higher Order Harmonic Balance Solutions for Nonlinear Aeroelastic Systems
Dimitriadis, Grigorios ULg

in Journal of Aircraft (2008), 45(2), 523-537

The Harmonic Balance method is a very useful tool for characterizing and predicting the response of nonlinear dynamic systems undergoing periodic oscillations, either self-excited or due to harmonic ... [more ▼]

The Harmonic Balance method is a very useful tool for characterizing and predicting the response of nonlinear dynamic systems undergoing periodic oscillations, either self-excited or due to harmonic excitation. The method and several of its variants have been applied to nonlinear aeroelastic systems over the last two decades. This paper presents a detailed description of several Harmonic Balance methods and a continuation framework allowing the methods to follow the response of dynamic systems from the bifurcation point to any desired parameter value, while successfully negotiating further fold bifurcations. The continuation framework is described for systems undergoing sub-critical and super-critical Hopf bifurcations as well as a particular type of explosive bifurcation. The methods investigated in this work are applied to a nonlinear aeroelastic model of a Generic Transport Aircraft featuring polynomial or freeplay stiffness nonlinearity in the control surface. It is shown that high order Harmonic Balance solutions will capture accurately the complete bifurcation behavior of this system for both types of nonlinearity. Low order solutions can become inaccurate in the presence of numerous folds in the Limit Cycle Oscillation branch but can still yield practical engineering information at a fraction of the cost of higher order solutions. Time domain Harmonic Balance schemes are shown to be more computationally expensive than the standard Harmonic Balance approach. [less ▲]

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See detailComment on Flutter Prediction from Flight Flutter Test Data
Dimitriadis, Grigorios ULg; Cooper, Jonathan E

in Journal of Aircraft (2006), 43(3), 862-863

In a previous paper entitled “Flutter Predictions from Flight Flutter Test Data” the authors applied a number of different flutter prediction methods to data from two simulated aeroelastic aircraft models ... [more ▼]

In a previous paper entitled “Flutter Predictions from Flight Flutter Test Data” the authors applied a number of different flutter prediction methods to data from two simulated aeroelastic aircraft models and compared the resulting flutter predictions. The two simulated models were a simple three-degree-of-freedom Hancock wing model and the Sim-2 model of a generic four-engined civil transport. One of the methods examined in the paper was the Nissim and Gilyard method (NGM). Because of difficulties encountered with the Sim-2 model, the authors failed to apply the NGM successfully to it, and only results for the Hancock model were presented in the paper. With the aid of Eli Nissim, the authors have now succeeded in applying the method to the Sim-2 model and to obtain quality flutter predictions from it. In this short Comment, the initial problems encountered will be described and then the solutions will be outlined. Finally, flutter predictions for the method will be presented and compared to the flutter predictions obtained from the other methods by Dimitriadis and Cooper. [less ▲]

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See detailFlutter Prediction from Flight Flutter Test Data
Dimitriadis, Grigorios ULg; Cooper, Jonathan E

in Journal of Aircraft (2001), 38(2), 355-367

The most common approach to flight flutter testing is to track estimated modal damping ratios of an aircraft over a number of flight conditions. These damping trends are then extrapolated to predict ... [more ▼]

The most common approach to flight flutter testing is to track estimated modal damping ratios of an aircraft over a number of flight conditions. These damping trends are then extrapolated to predict whether it is safe to move to the next test point and also to determine the utter speed. In the quest for more reliable and efficient flight flutter testing procedures, a number of alternative data analysis methods have been proposed. Five of these approaches are compared on two simulated aeroelastic models. The comparison is based on both the accuracy of prediction and the efficiency of each method. It is found that, for simple aeroelastic systems, the Nissim and Gilyard method (Nissim, E., and Gilyard, G. B., “Method for Experimental Determination of Flutter Speed by Parameter Identification,” AIAA Paper 89-1324, 1989) yields the best flutter predictions and is also the least computationally expensive approach.However, for larger systems, simpler approaches such as the damping fit and envelope function methods are found to be most reliable. [less ▲]

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