Application of Higher-Order Harmonic Balance to Non-Linear Aeroelastic Systems Dimitriadis, Grigorios ; ; in Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2006, May) The influence of non-linearities on modern aircrafts is becoming of increasing impor- tance. The ability to accurately characterise LCOs and to predict at which speed they occur is very important. Higher ... [more ▼] The influence of non-linearities on modern aircrafts is becoming of increasing impor- tance. The ability to accurately characterise LCOs and to predict at which speed they occur is very important. Higher Order Harmonic Balance (HOHB) methods have attracted some interest from the aeroelastic community over the last two decades. Such methods carry the promise of high quality stability prediction and Limit Cycle Oscillation (LCO) amplitude and frequency prediction for non-linear aeroelastic systems. In this paper, a Higher Order Harmonic Balance scheme is devised to extend the effectiveness of the method to systems undergoing secondary Hopf bifurcations. It is shown that the proposed harmonic shifting technique can allow the HOHB method to accurately estimate both branches of limit cycles occurring after the second bifurcation. [less ▲] Detailed reference viewed: 67 (1 ULg)Identification of Non-Linear Dynamic Systems using an Expert Approach ; Dimitriadis, Grigorios ; in Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2006, May) An Expert System approach for the identification of non-linear systems is presented. The Expert System is an attempt to bring order into the non-linear system identification process. The final objective ... [more ▼] An Expert System approach for the identification of non-linear systems is presented. The Expert System is an attempt to bring order into the non-linear system identification process. The final objective is to deliver a parsimonious mathematical model of the dy- namical system under investigation. It works by defining the key stages of the procedure and iterating between them if necessary. It takes advantage of numerous methodologies to accomplish the tasks in each of the stages and uses the results from many of them. The Expert System applies the excitation forces appropriate to each method and analyses the responses. Each stage ends with a set of recommendations that can be used to begin the next stage. The Expert System is applied to a simple non-linear dynamic system. It is shown that the Expert System procedure can automatically detect, locate and quantify the non- linearity using its array of techniques. Furthermore, it can choose a suitable model struc- ture, select appropriate terms and estimate the model parameters using an extensive set of rules. The resulting identified model is validated and shown to be an accurate represen- tation of the experimental system. [less ▲] Detailed reference viewed: 24 (0 ULg)Comment on Flutter Prediction from Flight Flutter Test Data Dimitriadis, Grigorios ; 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 ▲] Detailed reference viewed: 145 (10 ULg)Vibration Testing and System Identification Dimitriadis, Grigorios Scientific conference (2005, December 16) This presentation is a summary of the recent activity of the Dynamics and Aeroelasticity Research Group of the University of Manchester on the subjects of Vibration Testing and System Identification. Detailed reference viewed: 40 (4 ULg)Flutter Clearance of a Non-linear aircraft ; ; Dimitriadis, Grigorios et al in Proceedings of the 2005 International Forum on Aeroelasticity and Structural Dynamics (2005, June) Flight flutter testing is always carried out under the assumption that aircraft are linear. Recently, this assumption has started to come under question, especially as far as military aircraft are ... [more ▼] Flight flutter testing is always carried out under the assumption that aircraft are linear. Recently, this assumption has started to come under question, especially as far as military aircraft are concerned. This paper deals with possible methodologies for flight flutter testing of aircraft that are no longer assumed linear. Simulated flight testing is performed for a simple non-linear aeroelastic system with cubic stiffness. The flutter speeds predicted using some of the classical linear flutter prediction methods as well as a non-linear method are compared. It is shown that, for non-linear system undergoing Hopf Bifurcations, classical linear flutter prediction can predict the flutter envelope with reasonable accuracy. However, fully non-linear system identification and stability analysis can not only predict the flutter point but also determine whether it is a linear or non-linear flutter point (i.e. whether divergent or Limit Cycle Oscillations will ensue). Additionally, the non-linear method can predict the amplitudes of LCOs that will occur post-critically. The application of the nonlinear method was successful for noise free data, but the problem of noise corruption still needs further investigation. [less ▲] Detailed reference viewed: 31 (1 ULg)Stability and LCO Amplitude Prediction for Aeroelastic Systems with Aerodynamic and Structural Nonlinearities Using Numerical Continuation ; Dimitriadis, Grigorios ; in RTO-MP-AVT-123 Flow-Induced Unsteady Loads and the Impact on Military Applications (2005, April) This paper deals with the prediction of stability boundaries and Limit Cycle Oscillation amplitudes for aeroelastic systems with nonlinear unsteady aerodynamic loads and/or nonlinearity in the structure ... [more ▼] This paper deals with the prediction of stability boundaries and Limit Cycle Oscillation amplitudes for aeroelastic systems with nonlinear unsteady aerodynamic loads and/or nonlinearity in the structure. The Numerical Continuation method is used to accurately predict bifurcation conditions and LCO amplitudes for aeroelastic systems with various types of nonlinearity without the need for extensive CFD calculations. It is shown that it is possible to completely characterise the stability of systems undergoing subcritical and supercritical bifurcations. The method is applied to a pitch-plunge airfoil subjected to transonic aerodynamics and freeplay structural nonlinearity. The results from this analysis are compared to those obtained from full numerical simulation to ensure their accuracy. [less ▲] Detailed reference viewed: 55 (3 ULg)Non-Linear Identification Using a Genetic Algorithm Approach for Model Selection ; ; et al in Proceedings of the 23rd International Modal Analysis Conference (2005, January) The Non-Linear Resonant Decay Method is an approach for the identification of non-linear systems with large numbers of degrees of freedom. The identified non-linear model is expressed in linear modal ... [more ▼] The Non-Linear Resonant Decay Method is an approach for the identification of non-linear systems with large numbers of degrees of freedom. The identified non-linear model is expressed in linear modal space and comprises the modal model of the underlying linear system with additional terms representing the non-linear behaviour. Potentially, a large number of these non-linear terms will exist but not all of them will be significant. The problem of deciding which and how many terms are required for an accurate identification has previously been addressed using the Forward Selection and Backward Elimination techniques. In this paper, a Genetic Algorithm optimisation is proposed as an alternative to those methods. A simulated 5-DOF lumped parameter non-linear system is used to demonstrate the proposed optimisation. The use of separate data sets for the identification and validation of the modal model is also investigated. It is found that the Genetic Algorithm approach yields significantly better results than the Backward Elimination and Forward Selection algorithms in many cases. [less ▲] Detailed reference viewed: 25 (0 ULg)Stability and Limit Cycle Oscillation Amplitude Prediction for Multi-DOF Aeroelastic Systems with Piecewise Linear Non-Linearities Dimitriadis, Grigorios ; ; in Proceedings of the 2004 International Conference on Noise and Vibration Engineering (2004, September) Discontinuous non-linearities such as freeplay and bilinear stiffness are often encountered in aeroelastic systems, sometimes as a result of wear and tear. It is important to predict the effect of such ... [more ▼] Discontinuous non-linearities such as freeplay and bilinear stiffness are often encountered in aeroelastic systems, sometimes as a result of wear and tear. It is important to predict the effect of such non-linearities on the dynamic behaviour of a system, so that adequate safety guidelines can be drafted. As a consequence, the prediction of the bifurcation behaviour of a system featuring a discontinuous nonlinearity is crucial. Additionally, the post-bifurcation behaviour of the system is also of interest since it may consist of relatively harmless Limit Cycle Oscillations (LCO) of low amplitude or of unexpected catastrophic high amplitude LCOs. In this paper the bifurcation and post-bifurcation behaviour of a simulated Multi-DOF aeroelastic system with bilinear and freeplay nonlinearities are investigated using the Harmonic Balance method and a novel method for the prediction of the bifurcation conditions and LCO amplitudes. The method is based on the fact that the nonlinearities investigated are piecewise linear. The ratios of the real parts of the system eigenvalues in the various ranges of the bilinear spring are used in order to infer LCO amplitude information. By means of a demonstration on a simulated aeroelastic system with piece-wise linear stiffness, it is shown that the proposed approach is successful in yielding the full bifurcation and post-bifurcation behaviour of the system. Comparison of the amplitude predictions obtained from the Harmonic Balance technique and the Piecewise Linearisation proposed approach show that the latter are more consistent and closer to the true amplitudes throughout the airspeed range. The bifurcation analysis is extended to the special case where the inner stiffness of the bilinear spring is equal to zero, i.e. freeplay stiffness. It is shown that the Piecewise Linear analysis fails to capture the bifurcation behaviour for this case, while the Harmonic Balance method still produces some accurate predictions. [less ▲] Detailed reference viewed: 36 (1 ULg)On the solution of the aeroelastic galloping problem ; Dimitriadis, Grigorios ; in Proceedings of the 2004 International Conference on Noise and Vibration Engineering (2004, September) A global stability analysis of the transverse galloping of a square section beam in a normal steady ow was performed. The analysis was applied to a mathematical model using experimentally measured ... [more ▼] A global stability analysis of the transverse galloping of a square section beam in a normal steady ow was performed. The analysis was applied to a mathematical model using experimentally measured stationary aerodynamic forces. The system was modelled as an ordinary differential equation with small non-linearity in the velocity term. Three methods are used for the stability analysis: 1. a harmonic balance approach, 2. normal form theory, 3. cell mapping. The resulting stability predictions were compared with each other and with results obtained from numerical integration. It is shown that the hysteretic stability of the non-linear aeroelastic oscillator was captured by all the methods. Additionally, the methods had a varying degree of success in predicting the amplitude of limit cycle oscillations undergone by the aeroelastic oscillator. [less ▲] Detailed reference viewed: 150 (0 ULg)Validating Blade Vibration Amplitudes from Blade Tip-Timing Data Analysis ; Dimitriadis, Grigorios in Vibrations in Rotating Machinery (2004, September) Blade Tip-Timing (BTT) is a method for the measurement of blade vibration in rotating bladed assemblies such as those found in turbomachinery. BTT data needs to be analysed by specially formulated methods ... [more ▼] Blade Tip-Timing (BTT) is a method for the measurement of blade vibration in rotating bladed assemblies such as those found in turbomachinery. BTT data needs to be analysed by specially formulated methods, to yield the vibration frequencies and amplitudes. Although such methods have been shown to recover frequencies successfully, they have not been validated experimentally for amplitude recovery. In the present paper an improved experimental procedure for amplitude measurement is described. The paper presents a comparison between the experimental observation of the blade vibration amplitudes and the answers obtained from the BTT data analysis methods, providing experimental evidence of the ability of these methods to extract the correct blade vibration amplitudes from BTT data. [less ▲] Detailed reference viewed: 145 (1 ULg)Subspace Monitoring of Multivariate Dynamic Systems ; ; Dimitriadis, Grigorios in Akay, A.; Arnas, O.; Cooper, J. E. (Eds.) et al Proceedings of 7th Biennial ASME Conference on Engineering Systems Design and Analysis (2004, July) In this article, the monitoring of continuous processes using linear dynamic models is presented. It is outlined that dynamic extensions to conventional multivariate statistical process control (MSPC ... [more ▼] In this article, the monitoring of continuous processes using linear dynamic models is presented. It is outlined that dynamic extensions to conventional multivariate statistical process control (MSPC) models may lead to the inclusion of large numbers of variables in the condition monitor. To prevent this, a new dynamic monitoring scheme, based on subspace identification, is introduced, which can (i) determine a set of state variable for describing process dynamics and (ii) produce a reduced set of variables to monitor process performance. This is demonstrated by an application study to a realistic simulation of a chemical process. [less ▲] Detailed reference viewed: 21 (0 ULg)Nonlinear System Identification using Interpolated Short Time Fourier Transform ; Dimitriadis, Grigorios in Akay, A.; Arnas, O.; Cooper, J. E. (Eds.) et al Proceedings of 7th Biennial ASME Conference on Engineering Systems Design and Analysis (2004, July) For the purpose of constructing the backbone of nonlinear systems, the Interpolated Short Time Fourier Transform (ISTFT) is proposed as a means to improve the estimation accuracy of the instantaneous ... [more ▼] For the purpose of constructing the backbone of nonlinear systems, the Interpolated Short Time Fourier Transform (ISTFT) is proposed as a means to improve the estimation accuracy of the instantaneous amplitudes and frequencies of response signals. It is shown that the backbone curves estimated by the ISTFT agree with theoretical backbone curves very well. Additionally, the restoring force can be reconstructed to specify the type of nonlinear stiffness. A curve-fitting technique is introduced to estimate the parameters of nonlinear systems on the basis of theoretical backbone curves. It is shown that a number of typical nonlinear stiffness functions such as cubic, bilinear and pre-compressed springs can be identified accurately using this new method. [less ▲] Detailed reference viewed: 35 (0 ULg)Identification and model Updating of a non-stationary vibrating system Dimitriadis, Grigorios ; ; et al in Akay, A.; Arnas, O.; Cooper, J. E. (Eds.) et al Proceedings of 7th Biennial ASME Conference on Engineering Systems Design and Analysis (2004, July) Non-stationary systems, which are commonly encountered in many fields of science, are characterized by time-varying features and require time-frequency methods for their analysis. This study considers the ... [more ▼] Non-stationary systems, which are commonly encountered in many fields of science, are characterized by time-varying features and require time-frequency methods for their analysis. This study considers the problem of identification and model updating of a non-stationary vibrating system. In particular, a number of identification methods and a model updating procedure are evaluated and compared through application to a time-varying “bridge-like” laboratory structure. The identification approaches include Frequency Response Function based parameter estimation techniques, Subspace Identification and Functional Series modelling. All methods are applied to both output-only and input-out-put data. Model updating is based upon a theoretical model of the structure obtained using a Rayleigh-Ritz methodology, which is updated to account for time-dependence and nonlinearity via the identification results. Interesting comparisons, among both identification and model updating results, are performed. The results of the study demonstrate high modelling accuracy, illustrating the effectiveness of model updating techniques in non-stationary vibration modelling. [less ▲] Detailed reference viewed: 42 (4 ULg)Multiple Frequency Analysis Methods for Blade Tip-Timing Data Analysis ; Dimitriadis, Grigorios Blade Tip-Timing (BTT) is a method for the measurement of blade vibration in rotating bladed assemblies such as those found in turbomachinery. The system aims to replace strain gauge technology. However ... [more ▼] Blade Tip-Timing (BTT) is a method for the measurement of blade vibration in rotating bladed assemblies such as those found in turbomachinery. The system aims to replace strain gauge technology. However all current BTT analysis methods fail to recover the correct frequencies when two blade modes are excited simultaneously by a synchronous vibration. In this paper, five new methods that can recover simultaneous frequencies from BTT data are presented. The methods are based on the auto-regressive approach. The approaches make use of data either from a single blade and single revolution or from multiple revolutions. Furthermore, some of the methods are designed to allow for the presence of measurement errors. The techniques are validated on three test cases in which simulated data was used. It is shown that most of the methods produce accurate estimates for the vibration frequency, even in the presence of significant noise levels, provided that a suitable amount of the response waveform is measured. The most consistent estimates are obtained from the methods that make use of data from multiple revolutions. [less ▲] Detailed reference viewed: 95 (3 ULg)Stability and Limit Cycle Oscillation Amplitude Prediction for Simple Nonlinear Aeroelastic Systems Dimitriadis, Grigorios ; ; in Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2004, April) The prediction of the bifurcation and post-bifurcation behaviour of nonlinear aeroelastic systems is becoming a major area of research in the aeroelastic community due to the need for improved transonic ... [more ▼] The prediction of the bifurcation and post-bifurcation behaviour of nonlinear aeroelastic systems is becoming a major area of research in the aeroelastic community due to the need for improved transonic aeroelastic prediction, the use of non-linear control systems, and new construction techniques that reduce the amount of inherent damping. In this paper, a novel application of the Centre Manifold Theorem is used to accurately predict bifurcation conditions and Limit Cycle Oscillation amplitudes for simple aeroelastic systems with various types of nonlinearity. A simple aeroelastic system with hardening cubic stiffness nonlinearity is considered and is demonstrated to display a wide variety of bifurcation phenomena. These make it dif cult for some of the standard existing methods, such as Normal Form, Cell Mapping and Tangential Linearisation, to quantify the Limit Cycle Oscillation amplitudes through the entire speed range of the system. Then, the proposed approach is introduced and applied to the same system. It is shown that it can accurately predict the limit cycle amplitudes of the system undergoing all types of bifurcation. Finally, the new technique is applied to the same system but with softening cubic stiffness nonlinearity. It is shown that the method can accurately predict both the static and dynamic divergence boundaries and that it can be used to draw a worst-case stability boundary, inside which the solution is always stable. [less ▲] Detailed reference viewed: 135 (3 ULg)Limit Cycle Prediction For Subsonic Aeroelastic Systems Using Nonlinear System Identification Dimitriadis, Grigorios ; ; in Ferman, M. A.; Petersson, B. A. T.; Rizzi, S. A. (Eds.) et al Proceedings of the VIII International Conference on Recent Advances in Structural Dynamics (2003, July) The prediction of aeroelastic instabilities caused by nonlinear unsteady aerodynamic forces acting on aircraft has recently become an important area of research. Emphasis is placed on the capability to ... [more ▼] The prediction of aeroelastic instabilities caused by nonlinear unsteady aerodynamic forces acting on aircraft has recently become an important area of research. Emphasis is placed on the capability to predict the occurrence of Limit Cycle Oscillations (LCOs) at both the design and prototype testing stages. In this paper, the prediction of LCOs is attempted for a simulated aeroelastic system subjected to nonlinear subsonic unsteady aerodynamic forces, using system identification. Response data from the simulated system are curve-fitted by means of a series of polynomial basis functions. This approach yields very accurate identified models of the actual system at individual flight conditions. These identified models are extrapolated to a global aeroelastic identified model. Using this model, the flight conditions at which LCOs occur is accurately predicted but the amplitude of the oscillations is underestimated. [less ▲] Detailed reference viewed: 14 (2 ULg)Nonlinear Aeroelastic Research at the Dynamics and Aeroelasticity Research Group Dimitriadis, Grigorios Conference (2003, June) This work is a presentation of the recent research in nonlinearity carried out at the Dynamics and Aeroelasticity Research Group (DARG) of the University of Manchester, School of Engineering Detailed reference viewed: 58 (0 ULg)Improvements of some analysis methods for flight flutter test data using unsteady aerodynamic considerations Dimitriadis, Grigorios in Proceedings of the 2003 International Forum on Aeroelasticity and Structural Dynamics (2003, June) To date the analysis of data from ight utter tests is routinely carried out under the assumption of steady or, at best, quasi-steady aerodynamics. This approach is favored mainly because of its simplicity ... [more ▼] To date the analysis of data from ight utter tests is routinely carried out under the assumption of steady or, at best, quasi-steady aerodynamics. This approach is favored mainly because of its simplicity. In this paper it is shown that, even for some very simple simulated aeroelastic systems, utter predictions that ignore the unsteadiness of aerodynamic loads can be signi cantly inaccurate. Then, two simple system identi cation techniques are proposed that can model both the steady and unsteady aerodynamic loads acting on an aeroelastic system in incompressible ow. These methods can be used in order to obtain a complete description of an aeroelastic system subject to unsteady aerodynamic forces, including its dependence on ight conditions. Finally, the new methods are applied to a simple simulated unsteady aeroelastic model. The resulting utter predictions are compared to those obtained from two standard ight utter test data analysis approaches and are shown to be signi cantly more accurate. [less ▲] Detailed reference viewed: 24 (0 ULg)On the use of control surface excitation in flutter testing ; ; et al in Proceedings of the 2003 International Forum on Aeroelasticity and Structural Dynamics (2003, June) Flutter testing is used to demonstrate that the aircraft flight envelope is flutter free. Response measurements from deliberate excitation of the structure are used to identify and track frequency and ... [more ▼] Flutter testing is used to demonstrate that the aircraft flight envelope is flutter free. Response measurements from deliberate excitation of the structure are used to identify and track frequency and damping values against velocity. In this paper, the common approach of using a flight control surface to provide the excitation is examined us ing a mathematical model of a wing and control surface whose rotation is restrained by a simple actuator. In particular, it is shown that it is essential to use the demand signal to the actuator as a reference signal for data processing. Use of the actuator force (or strain) or control angle (or actuator displacement) as a reference signal is bad practice because these signals contain response information. It may also be dangerous in that the onset of flutter may not be seen in the test results. Control sur face flutter is of particular concern. [less ▲] Detailed reference viewed: 71 (0 ULg)On the use of control surface excitation in flutter testing ; ; et al in Proceedings of the Institution of Mechanical Engineers - Part G - Journal of Aerospace Engineering (2003), 217(6), 317-332 Flutter testing is aimed at demonstrating that the aircraft flight envelope is flutter free. Response measurements from deliberate excitation of the structure are used to identify and track frequency and ... [more ▼] Flutter testing is aimed at demonstrating that the aircraft flight envelope is flutter free. Response measurements from deliberate excitation of the structure are used to identify and track frequency and damping values against velocity. In this paper, the common approach of using a flight control surface to provide the excitation is examined using a mathematical model of a wing and control surface whose rotation is restrained by a simple actuator. In particular, it is shown that it is essential to use the demand signal to the actuator as a reference signal for data processing. Use of the actuator force (or strain) or control angle (or actuator displacement) as a reference signal is bad practice because these signals contain response information. It may also be dangerous in that the onset of flutter may not be seen in the test results. [less ▲] Detailed reference viewed: 39 (3 ULg) |
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