Aeroelastic System Research Articles

Adaptive Fuzzy Sliding Mode Controller Design Using a High-Gain Observer for a Nonlinear Aeroelastic System under Unsteady Aerodynamics

Adaptive Fuzzy Sliding Mode Controller Design Using a High-Gain Observer for a Nonlinear Aeroelastic System under Unsteady Aerodynamics

Mechanism of airfoil stall flutter: New insights from global linear stability analysis

Stall flutter is a self-excited aeroelastic vibration phenomenon that occurs in lifting systems near the stall angle of attack, characterized by the distinct single-degree-of-freedom behavior. Despite its significance, this phenomenon remains not fully understood and is often vaguely attributed to nonlinear effects. To address this gap, the present study aims to reveal the underlying fluid–structure interaction mechanisms of stall flutter through global linear stability analysis (LSA). For this purpose, a reduced-order model (ROM)-based aeroelastic stability analysis framework is established using the autoregressive with exogenous input method. The ROM-based aeroelastic model provides a low-order representation of the coupled dynamics near the equilibrium steady state and can accurately capture the stability characteristics of the fluid-elastic system. It is found that as the angle of attack approaches the static stall angle, a low-frequency weakly stable fluid mode emerges, whose frequency is sufficiently lower than that of the von Kármán vortex shedding. The interaction between this fluid mode and the structure mode ultimately leads to the instability of the aeroelastic system at high reduced velocities, which is the fundamental cause of stall flutter. Moreover, dynamic mode decomposition is employed to successfully extract the spatial coherent structures and frequency characteristics of this low-frequency fluid mode, thereby confirming the validity of the LSA results. Further analysis indicates that, as the angle of attack decreases, this low-frequency fluid mode gradually weakens and eventually degenerates into more stable non-oscillatory fluid modes, resulting in structural stabilization and the cessation of stall flutter. Overall, the linear dynamic model accurately predicts the onset of instability and the vibration frequency of the airfoil, which challenges the traditional nonlinear perspectives and supports the feasibility of using linear control theory for stall flutter suppression in future research.

Active maneuver load alleviation for a pitching wing via spanwise-distributed camber morphing

This paper presents the design and verification of a nonlinear model inversion (NMI) controller for the maneuver load alleviation of a pitching oscillating wing based on spanwise-distributed active camber morphing. Recurrent neural networks (RNNs) are used to predict nonlinear and unsteady aerodynamic forces due to wing's large amplitude pitching maneuver, and a fully connected neural network is introduced to build the dynamic inversion of the aeroelastic system for control law design. The inversed system is concatenated with a PI controller to assemble a nonlinear active controller. The controller is first utilized in an offline environment for a 1DoF pitching finite-span wing with spanwise-distributed active camber morphing and then verified in CFD-based fluid-structure-control coupling simulation. The results show that the offline controller could eliminate the maneuver load. In the online CFD-based fluid-structure-control simulation, the bending moment can be alleviated by 38%.

Reduced-Order Sliding Mode Observer-Based Backstepping Integral Logarithmic Sliding Mode Control: Application to Wing Aeroelastic System

Reduced-Order Sliding Mode Observer-Based Backstepping Integral Logarithmic Sliding Mode Control: Application to Wing Aeroelastic System

Data-Driven Method for Nonlinear Modal Interaction Identification in Fighter Aircraft

The purpose of this paper is to report a new data-driven analysis methodology for identifying nonlinear modal interactions and its application to aeroelastic wind-tunnel data from a generic fighter configuration, which reveals global modal interactions in this system caused by multiple resonance capture events initiated by local nonlinearities. It is shown that during supersonic testing at the Transonic Dynamics Tunnel, vibro-impacts at the embedded external fuel tank shakers on the inboard underwing stations of the generic fighter introduce strong nonlinearity that gives rise to nonlinear modal interactions. Specifically, time–frequency analysis of the acceleration data demonstrates that 6∶5 and 7∶6 transient resonance captures occur across the aircraft exclusively during this vibro-impact forcing window. Further analysis suggests that these resonance captures are dependent on Mach number. These results show experimentally that local vibro-impacts can cause global nonlinear effects in an aeroelastic system and that these effects can be identified using the new methodology herein. The data-driven analysis scheme employed shows applicability to full-aircraft flight test data for identifying nonlinear modal interactions without knowledge of the precise nonlinear contributors.

Gust response alleviation of the aircraft wing aeroelastic systems in supersonic flows using nonlinear energy sink

In order to reduce the gust response level of the aircraft wing aeroelastic systems in supersonic flows, the nonlinear energy sink (NES) is introduced into the aeroelastic system, and the effect of the nonlinear energy sink on the aeroelastic gust response is studied. The gust response dynamic model without and with NES is established by Lagrange equation, considering the cubic nonlinear characteristics of both plunge and pitch stiffness. The piston theory model as well as the '1-cos' model are employed to describe the unsteady aerodynamic load and the gust velocity, respectively. Besides, the comparison study of the gust response amplitude and energy characteristics of the wing aeroelastic systems with and without NES are analyzed. For systems with NES, the amplitude of gust dynamic response decreases rapidly, while vibration can be transmitted to the NES mechanism and causing its vibration. From an energy perspective, about 72.15 % of the original vibration energy has been transferred into NES, and further consumed through its damping. The influence of NES parameters, such as frequency ratio, mass ratio, damping ratio, and installation position on gust response, is discussed. Numerical simulations demonstrate that: as the frequency ratio, damping ratio and mass ratio increase, the dynamic response amplitude of the aeroelastic system decays faster, and the energy transferred from the wing system also increases. In addition, an optimal relative distance for the installation of NES can be found with best gust alleviation effect. The influence of nonlinear energy sink on the targeted transfer of vibration energy in aeroelastic systems are analyzed under different working conditions. The NES shows great gust alleviation effect and good robustness under different flight speeds, gust intensities, and gust lengths.

Efficient Forced Response Minimization Using a Full-Viscosity Discrete Adjoint Harmonic Balance Method

A forced response induced by inlet distortion and blade row interactions can lead to high-cycle fatigue failure, especially when the unsteady excitation frequency is close to the natural vibration frequency of a blade. This paper presents the study of forced response sensitivity analysis and minimization using a full-viscosity unsteady discrete adjoint method. The goal is to improve the aeroelastic performances of turbomachinery blades and simultaneously constrain/improve aerodynamic performances. The decoupled modal reduction method is used to compute the forced response, which is considered the objective function in adjoint-based design optimization. To analyze aeroforcing and aerodamping flow and adjoint fields efficiently, the harmonic balance method and its adjoint counterpart developed by an automatic differentiation tool are applied. Two cases—the NASA Rotor 67 with inlet distortion and a three-row configuration with multiple fundamental frequencies in the second row—are used to demonstrate the effectiveness of the aerodynamic and aeroelastic coupled design optimization system developed in this work. For the latter case, the Fourier-transform-based method that first decomposes and then matches the time and space modes at two sides of an interface is used for interface coupling. The almost-periodic Fourier transform method is used to determine the time instances for cases with multiple fundamental frequencies.

Effect of Hopf-Hopf bifurcation on the post-flutter behavior of a three-degree-of-freedom airfoil

The post-flutter dynamics of a three-degree-of-freedom nonlinear airfoil with unsteady aerodynamics are investigated based on the Hopf-Hopf bifurcation theory. Many prior works have relied on Hopf bifurcation theory to predict flutter behavior in airfoil systems. Although this approach facilitates flutter prediction and characterization of post-flutter behavior in numerous scenarios, it may be invalid in specific instances, such as when the Hopf bifurcation of the system degenerates. Therefore, this study focuses on a classical degenerate case of Hopf bifurcation in airfoil systems, specifically the Hopf-Hopf bifurcation. We show that the system undergoes various Hopf-Hopf bifurcations under specific parameter conditions as the center of gravity shifts. The local dynamics near the Hopf-Hopf bifurcation points are represented, including quasiperiodic oscillations on a three-dimensional torus. The airfoil begins to oscillate quasiperiodically after the airflow speed crosses specific Hopf-Hopf bifurcation points. The study also uncovers complex quasiperiodic crises and quasiperiodic hysteresis loops, which have not been reported in previous studies of aeroelastic systems. Then, many singularities and bifurcation curves are obtained near the Hopf-Hopf bifurcation point by semiglobal unfolding. Furthermore, the influence of stall effects on the bifurcation structure of the system is represented. It is shown that the types of Hopf-Hopf bifurcations may vary with the changes of stall effects, influencing the system's semiglobal bifurcation structures consequently. For all Hopf-Hopf bifurcation scenarios, stall effects affect one of the Neimark-Sacker bifurcation curve structures unfolded from the Hopf-Hopf bifurcation point significantly, while the other Neimark-Sacker bifurcation curve experiences minimal impact from stall effects. Moreover, a large nonlinear stall coefficient will postpone the onset of quasiperiodic/chaotic oscillations.

Optimal Sparsity in Nonlinear Nonparametric Reduced Order Models for Transonic Aeroelastic Systems

Machine learning and artificial intelligence algorithms typically require a large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden associated with generating data, the usability of such methods has been limited to highly simplified aeroelastic systems. This paper presents a novel approach for the identification of optimized sparse higher-order polynomial-based aeroelastic reduced order models (ROMs) to significantly reduce the amount of training data needed without sacrificing fidelity. Several sparsity promoting algorithms are considered, including rigid sparsity, least absolute shrinkage and selection operator (LASSO) regression, and orthogonal matching pursuit (OMP). The study demonstrates that through OMP, it is possible to efficiently identify optimized s-sparse nonlinear aerodynamic ROMs using only aerodynamic response information. This approach is exemplified in a three-dimensional aeroelastic stabilator model experiencing high-amplitude freeplay-induced limit cycles. The comparison shows excellent agreement between the ROM and the full-order aeroelastic response, including the ability to generalize to new freeplay and velocity index values, with online computational savings of several orders of magnitude. The development of an optimally sparse ROM extends previous higher-order polynomial-based ROM approaches for feasible application to complex three-dimensional nonlinear aeroelastic problems, without incurring significant computational burdens or loss of accuracy.

Analytical Linearization of Aerodynamic Loads in Unsteady Vortex-Lattice Method for Nonlinear Aeroelastic Applications

This paper presents the analytical linearization of aerodynamic loads (computed with the unsteady vortex-lattice method), which is formulated as tangent matrices with respect to the kinematic states of the aerodynamic grid. The loads and their linearization are then mapped to a nonlinear structural model by means of radial-basis functions, allowing for a two-way strong interaction scheme. The structural model comprises geometrically exact beams formulated in a director-based total Lagrangian description, circumventing the need for rotational degrees of freedom. The structural model is spatially discretized into finite elements and temporally discretized with the help of an implicit scheme that identically preserves momenta and energy. The resulting nonlinear discrete equations are solved by applying Newton’s method, requiring calculating the Jacobians of the whole aeroelastic system. The correctness of the linearized loads is then shown by direct comparison with their numerical counterparts. In addition, we employ our strongly coupled aeroelastic model to investigate the nonlinear static and dynamic behavior of a suspension bridge. With this approach, we successfully investigate the numerical features of the aeroelastic system under divergence and flutter conditions.

Nonlinear-Model-Inversion Control for Stall-Flutter Suppression of an Airfoil via Camber Morphing

This paper presents a nonlinear-model-inversion control law to suppress stall flutter of an airfoil with active trailing-edge morphing. First, a nonlinear aeroelastic model is proposed utilizing two nonlinear autoregressive neural networks with exogenous inputs , which are used to predict aerodynamic moments on an airfoil due to large-amplitude oscillation and camber morphing, respectively. Afterward, a nonlinear-model-inversion control system is designed upon the mentioned aeroelastic system to suppress stall flutter via the camber morphing. A fluid–structure–control (FSC) coupling strategy is developed with structure and control systems embedded in the high-fidelity computational-fluid-dynamics environment to validate the control effect. The FSC high-fidelity simulations show that the nonlinear-model-inversion controller can suppress pitching oscillation completely, whereas a linear proportional–derivative controller without time delay only performs a limited suppression rate by 25.6%. The flowfield evolution result infers that the active camber morphing can generate a converse training-edge vortex, which counteracts the leading-edge vortex during stall flutter. From the perspective of an energy hysteresis, active camber morphing works well by converting injected aerodynamic energy from positive to negative.

Hysteresis behavior and generalized Hopf bifurcation in a three-degrees-of-freedom aeroelastic system with concentrated nonlinearities

A three-degrees-of-freedom aeroelastic system with concentrated structural nonlinearities is considered. The aerodynamic loads in the model are simulated by using unsteady aerodynamic forces. First, we evaluate the linear stability region of the aerodynamic system employing the Lienard–Chipart criterion so that the stability boundaries of the center of gravity position and the uncoupled pitch natural frequency are obtained. Next, we present the distribution of the first Lyapunov coefficient l1 in the parameter space by using the Poincaré projection method to determine the type of Hopf bifurcation (subcritical or supercritical). We identify three types of hysteresis loops associated with Hopf bifurcations: the first type contains one stable equilibrium point and one stable limit cycle, the second type consists of one stable equilibrium point and two stable limit cycles, and the third type comprises two stable limit cycles. Nonlinear analysis shows that the variations in hysteresis loop types are mainly caused by the nonlinear flutter critical points, namely the saddle–node bifurcation points of limit cycles. Furthermore, we determine a degenerate Hopf bifurcation type known as generalized Hopf bifurcation (Bautin bifurcation) and its corresponding second Lyapunov coefficient, l2. Subsequently, we conduct nonlinear flutter analyses for positive and negative values of l2 by using bifurcation diagrams and phase portraits. The results show that when the uncoupled pitch natural frequency is used as the control parameter, the occurring generalized Hopf bifurcations are all supercritical (l2<0). However, when the center of gravity position is used as the control parameter, the generalized Hopf bifurcations that occur have both supercritical and subcritical (l2>0) modes.

Parameterization of nonlinear aeroelastic reduced order models via direct interpolation of Taylor partial derivatives

The identification of optimally sparse Taylor partial derivatives presents a new opportunity in efficient nonlinear model reduction for complex aeroelastic systems. Unfortunately, for this class of reduced order model (ROM), the robustness that is observed in the linear regime to parameters including; dynamic pressure, control hinge linear stiffness, or even freeplay, can be quickly compromised in the nonlinear regime. In this paper, the nonlinear sensitivity of selected critical parameters is addressed by interpolating a library of nonlinear unsteady aerodynamic ROMs across a compact subspace in dynamic pressure and freeplay magnitude. The ROM, based on Lagrange interpolation of sparse higher-order Taylor partial derivatives, demonstrates excellent precision in modelling high amplitude transonic limit cycle oscillations for an all-movable wing with freeplay, capturing the LCO region (up to 96% of the linear flutter boundary), and for a range of freeplay values.

Impact of actuation and sensor measurement delays on stability of real-time hybrid aeroelastic simulation system

AbstractThis paper is focused on the stability of real-time hybrid aeroelastic simulation systems for flexible wings. In a hybrid aeroelastic simulation, a coupled aeroelastic system is ‘broken down’ into an aerodynamic simulation subsystem and a structural vibration testing subsystem. The coupling between structural dynamics and aerodynamics is achieved by real-time communication between the two subsystems. Real-time hybrid aeroelastic simulations can address the limitations associated with conventional aeroelastic testing performed within a wind tunnel or with pure computational aeroelastic simulation. However, as the coupling between structural dynamics and aerodynamics is completed through the real-time actuation and sensor measurement, their delays may inherently impact the performance of hybrid simulation system and subsequently alter the measured aeroelastic stability characteristics of the flexible wings. This study aims to quantify the impact of actuation and sensor measurement delays on the measured aeroelastic stability, e.g. the flutter boundary, of flexible wings during real-time hybrid simulations, especially when different aerodynamic models are implemented.

Self-induced non-synchronous resonance phenomena and stability in reduced aero-elastic system

The paper is aimed at the parametric dynamic analysis of the two degrees of freedom (DoF) phenomenological model of aero-elastic interaction between a friction-damped flexible mounted body and a flowing fluid. A coupled system of a linear structure oscillator and the van der Pol based wake oscillator is introduced. Firstly, the complex eigenvalue problem is used for the comprehensive analysis of frequency lock-in, veering and crossing areas from the structural mode stability point of view. Further, an in-depth analysis of the fully nonlinear model based on the numerical continuation method is presented. The analysis focuses on non-synchronous vibration in the resonance areas. Attention is paid to the investigation of transition mechanisms to frequency lock-in and frequency veering in the structural response. In experimental studies, the amplitude and frequency jumps are observed. Here, we show that the origin of these jump phenomena results from the mutual coexistence of two stable solutions, which form a hysteresis region, which can be found in experimentally gained data. Moreover, the influence of structure friction-damping on nonlinear response is evaluated. The proposed phenomenological model is validated concerning two different experimental-based investigations.

Feasible model-order reduction approach for analysis of composite rotor blades based on geometrically exact beam formulation

This paper presents a novel and practical reduced-order model (ROM) approach designed specifically for analyzing composite rotor blades, leveraging the geometrically exact beam formulation. The slender nature of rotor blades necessitates aero-structure coupled analysis to precisely predict their response, which involved numerous iterative computations. By capturing large displacements and rotations, this approach enhances the accuracy of blade behavior predictions under operational conditions. To address the computational demands of large-scale analyses, a ROM technique that effectively reduces system dimensionality while preserving critical structural features is introduced. The proposed method is then applied to the aero-structure interaction analysis of a hingeless hovering rotor trim, incorporating geometrical nonlinearity and centrifugal effects. The analysis results demonstrate that the ROM accurately captures the dynamics of these complex aeroelastic systems while significantly reducing computational costs. This approach exhibits significant potential for various aerospace applications, particularly in the design and analysis of structures undergoing geometrical nonlinear behavior and rotation-induced loads.

Wind tunnel bench test of a pitch-and-plunge aeroelastic model undergoing nonlinear post-flutter oscillations

The nonlinear post-flutter aeroelastic behavior of a classical pitch-and-plunge airfoil model in low-speed wind tunnel bench tests is reported in this study for a range of airflow speeds where stable oscillations are observed. An experimental airfoil prototype is designed, characterized and evaluated. Time domain data of the airfoil motion as well as other pertinent frequency and bifurcation characteristics are presented for different values of airflow speed, starting at the critical linear flutter speed of the airfoil model and increasing up to the sudden manifestation of violent unstable oscillations (when the test is interrupted for the safety of the structural apparatus). Stable post-flutter nonlinear oscillations, mainly attributed to the dynamic stall phenomenon and in a lesser degree to hardening structural effects, are observed for a range of airflow speeds starting at the neutral stability boundary of the aeroelastic system. The amplitudes of oscillation increase with increasing airflow speed and settle onto a limit-cycle. The coupled frequency of oscillation is dominated by the plunge degree-of-freedom and also increases with increasing airflow speed. The observed critical airfoil cut-in speed of limit-cycle onset is about 8.1 m/s (reduced speed of 5.1), and the observed cut-out speed of unstable response is about 9.5 m/s (reduced speed of 6.0). This work contributes with the literature of Aeroelasticity by presenting the realization, evaluation, and wind tunnel test data of a pitch-and-plunge airfoil model undergoing nonlinear post-flutter oscillations that may be useful to support other studies for verification purposes of eventual numerical simulations of similar aeroelastic systems.

Active Flutter Suppression: Quantification of Performance Loss Due to Actuator Saturation

Active flutter suppression technologies have the potential to lead to major weight savings while keeping the envisaged flight envelope for the future generation of commercial aircraft. Since the stabilization of aeroelastic systems undergoing flutter instabilities is strongly affected by actuators’ characteristics and delays in the closed loop, the degradation of closed-loop performance due to actuators’ nonlinearities must be thoroughly understood. Comparisons between the region of attraction and the controllable region can support the quantification of performance loss due to common actuators’ nonlinearities, such as amplitude and rate limits. At first, this paper illustrates a numerically robust algorithm for the full characterization of the controllable region of a generic unstable system under input amplitude and rate constraints. Secondly, the concept of region of attraction is expanded to assess the boundedness of the closed-loop response in the presence of input saturation and atmospheric disturbances. These concepts are here employed to define two nonlinear performance measures that quantify the performance loss due to actuators’ saturation in an unstable aeroelastic system stabilized by a flutter suppression controller. The approach is demonstrated on a realistic aeroelastic system for which different H2 and H∞ output feedback controllers are synthesized to augment the damping of the critical flutter mode.

A generalized wind turbine cross section as a reduced-order model to gain insights in blade aeroelastic challenges

In this work, we present an approach to study the aeroelastic stability of a wind turbine by focusing on the dynamics of a blade cross section. We present a methodology to obtain a reduced-order model of the blade dynamics in the form of generalized cross-sectional quantities that approximates the aerodynamic and structural properties of the full blade. The motivation for the work is to gain a physical understanding of the influence of aerodynamic models such as dynamic wake and dynamic stall on the frequency and damping of the structure using a reduced-order model with low computational cost. The model may be coupled to two-dimensional computational fluid dynamics softwares or engineering unsteady airfoil aerodynamics models accounting for dynamic wake and dynamic stall. In the latter case, we can obtain monolithic state-space forms of the aeroelastic system of equations, which simplifies the determination of the modal parameters and therefore the study of stability. The work investigates wind turbines in operation or at standstill, where vortex-induced vibrations and stall-induced vibrations, respectively, might be an issue. The implementation is made available as part of the open-source Python package WELIB and as part of the open-source unsteady aerodynamic driver of OpenFAST.

On a nonlinear behavior of an aeroelastic system with quartic stiffness

On a nonlinear behavior of an aeroelastic system with quartic stiffness