Aeroelastic System Research Articles

Nonlinear FE aeroelastic analysis of membrane airfoils with fixed and elastic supports

This paper presents a nonlinear aeroelastic analysis of membrane airfoils using the finite element method. The model uses the aerodynamic potential flow models based on the Prandtl–Glauert and Theodorsen’s thin-airfoil theories. The structural model accounts for the nonlinear strain due to the membrane deformation. The final aeroelastic system is presented in the time-domain which enables both static and transient response analysis. A comparison between the linear and the nonlinear aeroelastic results is presented. The effect of the elastic supports and their stiffness ratio on the aeroelastic characteristics is also investigated for static and dynamic responses due to step or harmonic wind loadings with a comparison to the fixed-ends membranes.

Reduced-Order Identification of Aeroelastic Systems with Constrained and Imposed Poles

This work investigates the identification of reduced-order state-space models from aeroelastic simulations of the interaction of a built-in structural finite element model and a linear aerodynamic model using unsteady potential theory. The objective is to propose and compare different new frequency-based identification methods operating on frequency response associated to the inputs and outputs of interest. The first methods considered are the Loewner interpolation method and a subspace algorithm. Subsequently, the paper introduces the possibility to apply stability constraints and to impose a certain number of poles estimated beforehand by the method in order to make the identified models closer to the true aeroelastic physics. To achieve this goal, new dedicated techniques are developed and subsequently validated on data generated by random state-space models of various orders, and on aeroelastic data obtained from structural and aerodynamic aircraft models.

Active disturbance rejection controller design for alleviation of gust-induced aeroelastic responses

This paper develops an active disturbance rejection control technology that uses the equivalent input disturbance (EID) approach to reduce the aeroelastic vibrations and structural loads caused by wind gusts. The influence of gust disturbance is evaluated by the EID estimator and actively compensated in the control input channel, giving a high disturbance rejection performance of the aeroelastic system. The suitable design of the state observer and low-pass filter is essential for the disturbance estimation and rejection. However, the conventional low-pass filter simply specified by a cutoff frequency may lead to a degraded estimation performance. To this end, a new structure of low-pass filter is proposed, and the design algorithms for the observer gain and filter parameters are also given. By specifying bandwidth constraints, the control system with guaranteed performance can be automatically generated. Numerical results show that for the acceleration measurement-based control, the proposed design method can achieve better disturbance estimation performance than that obtained by the conventional one, resulting in smaller gust responses. Finally, the proposed design method is further extended to the folding wing parameter-varying system. A parameterized version of the EID-based controller is constructed by using the concept of gain-scheduling. It is demonstrated that the gust responses can be significantly reduced in the entire range of folding angle. This study provides an effective solution for gust alleviation of the aeroelastic system with fixed or variable configurations.

Parametric modeling and analysis of transonic aeroelastic systems based on incremental learning

The aerodynamic reduced order model (ROM) is an effective tool for predicting unsteady aerodynamics and aeroelastic responses with high accuracy and low computational costs. However, traditional aerodynamic ROMs with respect to different flow conditions are lack of robustness. How to enhance dramatically the generalization capability of aerodynamic ROMs should be further studied. This paper presents three parametric ROMs based on the least squares support vector regression algorithm (LS-SVR) and two incremental learning algorithms. LS-SVR is used to establish the relationship between aerodynamic inputs and outputs based on training data from high-fidelity flow simulations. And the Mach number is considered as an additional system input to account for varying flow conditions. The main contribution of incremental learning algorithms based on LS-SVR is that it does not need to reconstruct the ROM when adding sample data. For incremental learning algorithm with forgetting mechanism, training samples are added in the manner of a time-window to improve training efficiency. To illustrate the performance of these ROMs, the aerodynamic and aeroelastic responses of a NACA 0012 airfoil with two degrees of freedom are investigated. The simulation results show that both unsteady aerodynamic results and aeroelastic responses computed by using the three ROM-based models agree well with the results of the high-fidelity simulation. The three proposed ROMs have better generalization capacity and modeling efficiency.

Nonlinear aeroelastic modeling and comparative studies of three degree of freedom wing-based systems

The effects of structural and aerodynamic nonlinearities are investigated on an aeroelastic system with three degrees of freedom, those being plunge, pitch, and flap motions using two different aerodynamic load representations. Stall effects are introduced using quasi-steady and unsteady aerodynamic representations. The effects of the unsteadiness of the flow and stall effects on the type of Hopf bifurcation and the limit cycle oscillations of the system are explored. A comparative study between the unsteady and quasi-steady representations from a nonlinear perspective is also carried out. Results from the linear analysis show that for this specific aeroelastic system, its linear characteristics are dependent on the aerodynamic representation and the system’s design. Additionally, the quasi-steady approximation of the aerodynamic loads results in an inaccurate prediction of the linear flutter speed. Furthermore, the nonlinear analysis shows the existence of an instability shift from the supercritical to the subcritical type, depending on the value of the stall coefficient, as well as that of the cubic nonlinearities, and is more dominantly for the case when the quasi-steady representation is considered. Results show that, even for small reduced frequencies and small angles of attack scenarios, the unsteady representation of aerodynamic loads is critical to correctly predict the flutter speed, instability type, and system’s dynamics.

Data-Driven Unsteady Aeroelastic Modeling for Control

Aeroelastic structures, from insect wings to wind turbine blades, experience transient unsteady aerodynamic loads that are coupled to their motion. Effective real-time control of flexible structures relies on accurate and efficient predictions of both the unsteady aeroelastic forces and airfoil deformation. For rigid wings, classical unsteady aerodynamic models have recently been reformulated in state space for control and extended to include viscous effects. Here, we further extend this modeling framework to include the deformation of a flexible wing in addition to the quasi-steady, added mass, and unsteady viscous forces. We develop low-order linear models based on data from direct numerical simulations of flow past a flexible wing at a low Reynolds number. We demonstrate the effectiveness of these models to track aggressive maneuvers with model predictive control while constraining maximum wing deformation. This system identification approach provides an interpretable, accurate, and low-dimensional representation of an aeroelastic system that can aid in system and controller design for applications where transients play an important role.

Composite Adaptive Control and Identification of MIMO Aeroelastic System with Enhanced Parameter Excitation

Composite Adaptive Control and Identification of MIMO Aeroelastic System with Enhanced Parameter Excitation

Flutter stability analysis of aeroelastic systems with consideration of hybrid uncertain parameters

Uncertainties are usually ubiquitous and of different sources, and especially hybrid uncertainties widely exist in the aeroelastic system including external loads and material properties. In this context, a novel numerical method for flutter stability analysis of aeroelastic systems considering hybrid uncertain parameters is proposed. Uncertain parameters in aeroelastic systems are characterized by stochastic and interval model, and the flutter analysis model with hybrid uncertain parameters is established. The interval-based probability density evolution method is then developed to capture the probability density function of the lower and upper bound of generalized eigenvalues. By introducing the virtual time parameter, the probability density evolution equation can be transformed into a standard form. Using the finite difference method and the total variation diminishing (TVD) scheme, the probability density function as well as the second-order statistical quantities of the lower and upper bound of the maximum real part of generalized eigenvalues are predicted efficiently. Thus, the stability of aeroelastic systems with hybrid uncertain parameters can be analyzed based on the probability distribution of the interval bound of the maximum real part of generalized eigenvalues. Two numerical examples demonstrate that the proposed method yields results consistent with Monte-Carlo simulation method and improve the computational efficiency.

Preset angle, aspect ratio, and stall representations effects on the aeroelastic responses of small-scale wind turbine blades

This work provides an inclusive nonlinear aeroelastic study on the effects of horizontal axis Small-Scale Wind Turbines (SSWTs)’s preset angle of attack as well as aspect ratio on its aerodynamic stability. For this purpose, an enhanced nonlinear reduced-order model is established and a state–space formulation for the aerodynamics of a comprehensive wing-based aeroelastic system is constructed. This representation captures the influence of the preset angle of attack where the blade no longer displays an oscillatory motion around its zero-equilibrium point in the post-flutter region, instead, a new equilibrium point is introduced to the system through the incorporation of the preset angle. The effect of the preset angle on the blade stability is investigated by jointly performing linear analyses that provide insights on this parameter’s influence on the onset of flutter, accompanied with nonlinear analyses that evaluate the latter design parameter’s effect on the blade bending and torsion amplitudes in the post-flutter regime. Additionally, the Duhamel’s principle specific to low angles of attack is extended to represent unsteady flows with non-conventional lift curves of low aspect ratio blades while considering different representations of the aerodynamic stall. Results show the significant effect of the preset angle on both the onset of flutter as well as the post flutter amplitudes where the higher the preset angle, the higher the flutter speed. Furthermore, this research effort also demonstrates the importance of accurate lift modeling since ill-evaluated lift characteristics leads to a potential over- or under-estimation of the blade’s torsional and bending amplitudes post-flutter, and the conventional 2π slope assumption frequently used in various reduced-order-models within the literature seldom predicts erroneous onset of flutter values as well as inaccurate amplitudes in the post-flutter regime especially for the case of low aspect-ratio systems.

Convolution/Volterra Reduced-Order Modeling for Nonlinear Aeroelastic Limit Cycle Oscillation Analysis and Control

A methodology for leveraging a combination of linear (through convolution integrals) and nonlinear (through Volterra series) reduced-order modeling (ROM) development was demonstrated on both a two- and three-degree-of-freedom (2-DOF and 3-DOF, respectively) aeroelastic system. The linear/nonlinear ROM approach was demonstrated against previous work in the field for a 2-DOF system and subsequently extended to a 3-DOF (flapped airfoil) system. Excellent agreement was demonstrated at limit cycle oscillation (LCO) onset (flutter) prediction between computational fluid dynamics, linear ROMs, and nonlinear ROMs. Although linear ROMs were sufficient to predict LCO onset, the nonlinear Volterra correction was required to estimate the amplitude of post-LCOs. Corrections that accounted for more coupling between degrees of freedom predicted the amplitudes more accurately. A study was undertaken to determine the minimal training set required to produce reasonable LCO amplitude estimates of the 3-DOF airfoil. A controller was also implemented in an effort to mitigate LCO onset and flutter divergence and to demonstrate the usefulness and power of leveraging the ROM for control design. A full-state feedback controller, tuned via a linear quadratic regulator (LQR), was shown to be effective in controlling the system below LCO onset. However, beyond LCO onset, this specific linear controller structure was observed to be ineffective in controlling the system. Future work will evaluate nonlinear control methods in which the ROM can be deployed as a part of the control system to update the LQR gains in a fully coupled approach.

Flutter Boundary Prediction Based on Structural Frequency Response Functions Acquired from Ground Test

Establishing an accurate, fast, and low-risk flutter boundary prediction method is of great significance for flight vehicle design. In this paper, a ground flutter boundary prediction method (GFBP) based on experimental structural frequency response functions (FRFs) is proposed. A low-order multi-input multi-output (MIMO) aeroelastic system is established by combining the structural FRFs acquired from a ground test and the calculated unsteady aerodynamic FRFs in physical coordinates. The multivariable Nyquist criterion is used to predict the flutter boundary. A fixed-root aluminum plate wing is selected as the research model. A GFBP experiment is carried out for the wing’s normal state, leading-edge clump weight state, and trailing-edge clump weight state. The feasibility and accuracy of the proposed method are verified by comparison with theoretical flutter results, in which the errors of flutter speed and frequency in the test statistics are no more than 1.7%. In a simulation model established by the proposed method, Monte Carlo simulation is used to study the influence of deviations in the mode frequency and damping of the structural FRFs and deviations in the positions of excitation and measurement points in the ground test. The experiment and simulation results show that the proposed method can predict the flutter boundary accurately with accurate positions of excitation and measurement points, and it has good robustness to deviations in the mode frequency and amplitude of the structural FRFs.

Data-driven optimization for flutter suppression by using an aeroelastic nonlinear energy sink

Aeroelastic systems are at risk of flutter instabilities which can lead to structural failure. Recently, an innovative design of nonlinear energy sink (NES) has been introduced to suppress flutter instabilities by adding a NES to the flap control surface as a nonlinear energy absorber resulting in a flap-NES. Optimal choice of flap-NES parameters, however, requires a comprehensive characterization of the nonlinear response of the system in the design space. Performing this nonlinear analysis using traditional approaches demands massive theoretical and computational efforts. This work is a foundational study of flap-NES-based flutter control of a typical pitch–plunge section and focuses on obtaining flap-NES parameters using a data-driven optimization algorithm. The optimization is based on a genetic algorithm combined with a recently introduced data-driven bifurcation forecasting method that allows constructing the bifurcation diagram of the system dynamics using limited time series data. Results of this study show that an optimal design of the flap-NES system results in an increased linear flutter speed, reduced post-flutter limit cycle oscillation amplitudes, and improved nature of the bifurcation diagram from subcritical to supercritical.

On the closure of Collar’s triangle by optical diagnostics

An experimental methodology is proposed to study aeroelastic systems with optical diagnostics. The approach locally evaluates the three physical mechanisms that produce the forces involved in Collar’s triangle, namely aerodynamic, elastic, and inertial forces. Flow and object surface tracers are tracked by a volumetric particle image velocimetry (PIV) system based on four high-speed cameras and LED illumination. The images are analysed with Lagrangian particle tracking techniques, and the flow tracers and surface markers are separated based on the different properties of their images. The inertial and elastic forces are obtained solely analysing the motion and the deformation of the solid object, whereas the aerodynamic force distribution is obtained with pressure from PIV techniques. Experiments are conducted on a benchmark problem of fluid–structure interaction, featuring a flexible panel installed at the trailing edge of a cylinder. Data are collected in the resonant regime, where the panel exhibits a two-dimensional motion. The estimation of inertial and elastic forces is obtained enforcing a high-order polynomial fit to the surface motion and deformation. The aerodynamic loads on the panel are challenged by the need to devise adaptive boundary conditions complying with the panel motion. The closure of Collar’s triangle yields overall residuals of about one-half of the inertial force taken as reference. The simultaneous measurement of the three forces paves the way to assessing the equilibrium of forces closing the Collar’s triangle. The latter can be intended for uncertainty evaluation or, when only two forces are measured, for estimation of the remaining Collar element.Graphical

Adaptive Sampling for Interpolation of Reduced-Order Aeroelastic Systems

A new strategy for the interpolation of parametric reduced-order models of dynamic aeroelastic systems is introduced. Its aim is to accelerate the numerical exploration of geometrically nonlinear aeroelastic systems over large design spaces or multiple flight conditions. The parametric reduced-order models are obtained from high-dimensional models by Krylov-subspace projection. They are subsequently interpolated to acquire realizations inexpensively anywhere in the parameter space, where having the state space as opposed to interpolating an output metric permits the use of linear analysis tools. The interpolation scheme is heavily conditioned by the available training points; thus, a novel methodology based on adaptive sampling and a combinatorial use of the available true-systems knowledge is presented, whereby we reuse all known data of the true models as different combinations of training and testing data to build statistical surrogates of the interpolation error across the parameter space and refine the sampling in those regions that need it. This minimizes the number of costly to evaluate function calls and ensures that parameter space regions are sampled according to the underlying system dynamics. The initial implementation of this adaptive sampling strategy is demonstrated on a very flexible wing with a complex stability envelope.

Experimental investigation on the synchronization characteristics of a pitch-plunge aeroelastic system exhibiting stall flutter.

This study focuses on characterizing the bifurcation scenario and the underlying synchrony behavior in a nonlinear aeroelastic system under deterministic as well as stochastic inflow conditions. Wind tunnel experiments are carried out for a canonical pitch-plunge aeroelastic system subjected to dynamic stall conditions. The system is observed to undergo a subcritical Hopf bifurcation, giving way to large-amplitude limit cycle oscillations (LCOs) in the stall flutter regime under the deterministic flow conditions. At this condition, we observe intermittent phase synchronization between pitch and plunge modes near the fold point, whereas synchronization via phase trapping is observed near the Hopf point. Repeating the experiments under stochastic inflow conditions, we observe two different aeroelastic responses: low amplitude noise-induced random oscillations (NIROs) and high-amplitude random LCOs (RLCOs) during stall flutter. The present study shows asynchrony between pitch and plunge modes in the NIRO regime. At the onset of RLCOs, asynchrony persists even though the relative phase distribution changes. With further increase in the flow velocity, we observe intermittent phase synchronization in the flutter regime. To the best of the authors' knowledge, this is the first study reporting the experimental evidence of phase synchronization between pitch and plunge modes of an aeroelastic system, which is of great interest to the nonlinear dynamics community. Furthermore, given the ubiquitous presence of stall behavior and stochasticity in a variety of engineering systems, such as wind turbine blades, helicopter blades, and unmanned aerial vehicles, the present findings will be directly beneficial for the efficient design of futuristic aeroelastic systems.

Vibration control and trajectory tracking for nonlinear aeroelastic system based on adaptive iterative learning control

Vibration control and trajectory tracking for nonlinear aeroelastic system of 2D airfoil of wind turbine subjected to flap-wise vibration and independent pitch motion, are investigated based on hydraulic pitch control and adaptive iterative learning (AIL) control. The aeroelastic system is simplified by an external slubber, the host material of which is a composite material with shape memory alloy (SMA) wires embedded in. The independent pitch motion is driven by two-way-rack cylinder and hydraulic servo valve. The control of divergent unstable motions is implemented by tracking the vibrations of the preset displacements. The control law of AIL algorithm combines iterative algorithm and proportional-derivative (PD) control. The control parameters of PD controller are adjusted by proportional-derivative control based on single neuron (PDC/SN) algorithm. Based on the convergence analysis of the iterative algorithm, the tracking results (including position tracking and speed tracking) of the iterative process are shown, and the convergence of the absolute values of the relative errors during tracking is verified. The experiment based on process control and a refined OPC Technology verifies the feasibility of the engineering application of the proposed algorithm in nonlinear aeroelasticity. The consistency between the real-time dynamic tracking process shown on the experimental panel and the theoretical tracking process illustrated by simulation verifies the effectiveness of the control algorithm for engineering application. The research implication for the design of current turbine manufacturers is that it provides a design idea of blade buffer based on smart materials, and an implementation idea for the engineering application of adaptive AIL algorithm.

Analysis, control, and optimization of aeroelastic systems: an introduction to the recent literature for the new investigator

Aeroelasticity studies the static and dynamic interaction between structural deformation and fluid forces. As a result, the aeroelasticity is usually divided into three parts: aerodynamics, structural response, and dynamics with statics as a special case. Instabilities may occur to this interaction (feedback) that lead to structural failure and, even when no instability occurs, the interaction may lead to degradation or improvement of the system performance. There are several unstable phenomena may occur for elastic bodies such as flutter, divergence, low cycle oscillation, buffet, and control surface reversal. These unstable phenomena can be classified as dynamic or static. The present work provides a tutorial for those newly encountering aeroelasticity and a review of the recent literature from this century (after 2000). This includes mathematical modelling and its applications to airplanes, rotor blades, energy harvesting, and the control, and optimization of aeroelastic systems. Recent research advances are summarized and some suggestions for future work are made.

Sloshing reduced-order model based on neural networks for aeroelastic analyses

A thorough understanding of the effects of sloshing on aircraft dynamic loads is of great relevance for the future design of flexible aircraft to be able to reduce their structural mass and environmental impact. Indeed, the high vertical accelerations caused by the vibrations of the structure can lead to the fragmentation of the fuel free surface. Fluid impacts on the tank ceiling are potentially a new source of damping for the structure that has hardly been considered before when computing the dynamic loads of the wings. This work aims at applying recently developed reduced-order models of sloshing to the case of a research wing to investigate their effects on the wing aeroelastic response under pre-critical and post-critical conditions. The vertical sloshing dynamics is considered using neural networks trained with experimental data from a scaled tank and then integrated into the aeroelastic system following a suitable scaling procedure. The results concern the aeroelastic response of the wing to gust input under pre-critical (flutter) conditions as well as post-critical conditions highlighting the onset of limit cycle oscillations caused by sloshing, the only nonlinear phenomenon modelled in the present simulation framework. Moreover, the load alleviation performances will be assessed for a typical landing input.

Parameter Identification Method for Nonsmooth Aeroelastic System

In this paper, a parameter identification method merged with the precise integration method and the predictor–corrector strategy is proposed to identify the parameters of a nonsmooth aeroelastic system quickly and accurately. Considering the aeroelastic system subject to unsteady aerodynamic force, the parameters that need to be identified include the structural and nonsmooth parameters. The work of this paper mainly includes three parts. First, based on the precise integration method and combined with the predictor–corrector strategy, a new technology that can accurately locate the switching point is proposed to obtain the response of the aeroelastic system with high precision. Then, the problem for identification of parameters of the nonsmooth aeroelastic system is modeled as a nonlinear least-squares problem between the measured data and the calculated response. A new strategy that can obtain the nonsmooth parameters sensitivity matrix accurately is proposed, and then the parameters are identified through the enhanced response sensitivity approach. Finally, the nonsmooth aeroelastic system with freeplay and hysteresis nonlinearity are taken as the numerical examples to demonstrate the feasibility and robustness of the present method.

Aeroelastic analysis and nonlinear characterization of three-degree-of-freedom systems with discontinuous nonlinearities

The effects of freeplay, multi-segmented, and impact nonlinearities in the pitch and control surface degrees of freedom on the nonlinear responses of a three-degree of freedom aeroelastic system are investigated to characterize the nonlinear behavior and possible bifurcations. The system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom, a nonlinear torsional spring in the pitch degree of freedom, and a control surface with a nonlinear spring in the trailing edge. The unsteady representation based on the Duhamel formulation is used to model the aerodynamic loads. Nonlinear characterization is performed to identify the system’s response, under different representations of the nonlinear springs, below the linear flutter speed. The results show that grazing/sliding bifurcations are present and nonlinear coupling of the system’s frequencies lead to complex responses including sudden transitions between harmonic and chaotic responses as the freestream velocity is increased. These responses, which include the sudden amplitude jumps, generation of higher harmonics and broadband oscillatory behavior, could result in catastrophic structural failures of aeroelastic systems even when operating below the linear flutter speed.