Aeroelastic Vibrations Research Articles

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.

Aeroelastic wave attenuation of UAV wing with smart metamaterial resonators

This paper proposes a UAV wing based on smart metamaterial resonators (smart meta-wing), and studies its vibration wave attenuation under aerodynamic loads. A novel aeroelastic transfer matrix, incorporating aerodynamic effects, is developed to analyze the wave propagation. The study examines the influence of smart resonators on the coupled flexural-torsional wave attenuation with and without aerodynamic effects. The findings reveal that a new bandgap (aeroelastic bandgap) is formed along with local bandgap (SR bandgap), effectively attenuating both flexural and torsional waves. Additionally, the bandgap behavior can be actively tuned by varying the control gain of smart resonators. The proposed smart meta-wing model and aeroelastic transfer matrix offer a novel approach for actively attenuating the aeroelastic vibration waves of UAV wings for desired frequency range.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety. This paper proposes the strongly nonlinear acoustic metamaterial (NAM) method to mitigate aeroelastic vibration in supersonic wing plates. We employ the cantilever plate to simulate the practical behavior of a wing. An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory. The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods. While presenting the flutter and post-flutter behaviors of the NAM wing, we emphasize more on the pre-flutter broadband vibration that is prevalent in aircraft. The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%–90%, while the post-flutter vibration is reduced by over 95%, and the critical flutter velocity is also slightly delayed. As clarified, the significant reduction arises from the bandgap, chaotic band, and nonlinear resonances of the NAM plate. The reduction effect is robust across a broad range of parameters, with optimal performance achieved with only 10% attached mass. This work offers a novel approach for reducing aeroelastic vibration in aircraft, and it expands the study of nonlinear acoustic/elastic metamaterials.

Mitigating aeroelastic vibration of strongly nonlinear metamaterial supersonic wings under high temperature

Mitigating aeroelastic vibration of strongly nonlinear metamaterial supersonic wings under high temperature

A Smart Wing Model: From Design to Testing in a Wind Tunnel with a Turbulence Generator

The paper concerns the technology of the design, realization, and testing of a flexible smart wing in a wind tunnel equipped with a turbulence generator. The system of smart wing, described in detail, consists mainly of: a physical model of the wing with an aileron; an electric servomotor of broadband with a connecting rod-crank mechanism for converting the rectilinear motion of the servoactuator into the aileron deflection; two transducers: an encoder for measuring the deflection of the control aileron and an accelerometer mounted on the wing to measure its bending and torsional vibrations; a procedure for determining the mathematical model of the wing by experimental identification; a turbulence generator in the wind tunnel; implemented ℋ∞ and LQG algorithms for active control of vibrations. The attenuation experimentally obtained for the aeroelastic vibrations of the wing, but also for those accentuated by the turbulence, reaches values of up to 50%.

Subsonic Aeroelastic Stability Analysis and Vibration Control of a Plate by Using Nonlinear Energy Sink

Vibration suppression and stability control are classic issues in the field of vibration and control. The nonlinear energy sink (NES) is an effective approach for vibration reduction proposed in recent years. It has the advantages of wide frequency vibration isolation properties and without inputting excessive energy. This paper focuses on the stability and passive vibration control of a plate in subsonic airflow by applying the NES. Two kinds of NESs with linear stiffness and with cubic stiffness are proposed and their vibration control performances are compared. The kinetic equations of the plate with NES are established by using the extended Hamilton principle and analyzed by the incremental harmonic balance (IHB) method. The advantages of the hybrid stiffness NES are demonstrated by comparing with the cubic nonlinear stiffness NES. From the results, the vibration suppression effect of the hybrid stiffness NES is more significant than the purely cubic one. However, the effective vibration reduction range of the cubic stiffness NES is wider than the hybrid one. The optimal design parameters of the NES and the effect of the installation position are also discussed.

Interaction of flutter and forced response in a low pressure turbine rotor with friction damping and mistuning effects

In modern LPT designs, which typically can assume a tolerable level of flutter, the simultaneous presence of forced response and flutter in different operation regimes becomes unavoidable. Current design rules rely on the linear superposition of vibration levels from the isolated problems. However, recent evidence from reduced order model calculations and from experiments suggests that this may be an over conservative approach. In order to check this finding, this study examines the flutter and forced response interaction in a realistic low pressure turbine rotor. A high fidelity model is used, and an efficient numerical method is implemented for the computation of the aeroelastic vibrations of the rotor with nonlinear friction effects at the blade-disk contact interfaces. A hybrid approach is used that combines a traveling wave description for the linear modes with a physical space representation for the displacement of the nonlinear contacts. The resulting equations are integrated in the time domain in order to account for the unknown flutter frequencies present in the response. Both tuned and mistuned configurations are considered, and it is confirmed that the actual response of the system is much smaller than that coming from the linear superposition of the separated effects.

Modelling of vortex-induced force and prediction of vortex-induced vibration of a bridge deck using method of multiple scales

With the increase of span length, long-span bridges become more flexible and susceptible to vortex-induced vibrations (VIV). Several models for vortex-induced force (VIF) and various methods for predicting VIV have been developed accordingly but without consensus. This paper uses the method of multiple scales, from a different angle of view, to analyze the general polynomial model for VIF and present a concise polynomial model for VIF and a simple method for predicting VIV of a bridge deck. The aeroelastic vibration of a deck section is simulated by the computational fluid dynamics (CFD) and the results are used to verify the concise polynomial model of VIF. The forced vibration of a deck section is also simulated by CFD to yield the simple method for predicting VIV together with the frequency response equation and the critical equation of VIV derived by the method of multiple scales. The results show that the even and cross terms of aerodynamic damping and stiffness in the general polynomial VIF model are small compared with the odd terms and can be thus omitted. The lock-in region and the amplitude of VIV of the deck section can be accurately predicted by the proposed simple method.

Enhanced piezoelectric energy harvesting performance using trailing-edge flap

This paper proposes a novel piezoelectric energy harvester attached with a trailing-edge flap under various installation angles, for enhancing the aeroelastic vibration and improving the harvesting performance. The mathematical models of the fluid-structure-electric coupled fields are derived, the simulation models of the multi-physical coupled fields of the harvester system with various installation angle flaps are established, and the experimental prototypes of the harvester are fabricated. The influences of the flap installation angles on the flow field and output characteristics are investigated theoretically, numerically, and experimentally. The results demonstrate that the flap stiffness and damping coefficients exert less influence on vibration characteristics and harvesting performance. The flap at a certain installation angle alters the flow field, affects the flow pattern, restricts the vortex shedding, and offsets the aerodynamic force and moment. A decrease in the flap installation angles results in increasing the vibration response and output performance. The obtained numerical results are in good agreement with the experimental and theoretical values, which verifies the effectiveness of the simulation model. The maximum plunge amplitude is 0.029 m and the output voltage is 15.51 V at 17.74 m/s and an installation angle of 0o. The enhancement ratio of the output voltage at 0o is up to 148.6% over 45o, which achieves better harvesting performance. The designed harvester system powers indirectly the pedometer for 104 s at 13.58 m/s. This research offers an essential foundation for achieving better tradeoffs in energy harvesting and vibration suppressing by appropriately selecting the flap installation angle.

Overview of System Identification Tool Advancements at Systems Technology, Incorporated

For nearly two decades, Systems Technology, Inc. has been investigating novel system identification methods and practical applications. Two such methods will be highlighted herein: 1) the use of wavelet-based scalograms to explore the nature of dynamic systems in both the time and frequency domains simultaneously; and 2) a method to estimate frequency, damping, and mode shapes for lightly damped aeroelastic modes exhibited across a variety of air vehicles. From past work, two scalogram-based metrics have evolved, which are the power frequency and inceptor peak power phase, that will be one focus of this paper. The power frequency provides a metric that considers not only the dominant frequencies of the signal of interest, such as the command input from a pilot, but also the power at those frequencies. For the inceptor peak power phase, scalograms are used to identify the peak input power of a pilot’s inceptor command signal that when compared against a pitch or roll rate phase angle at the peak frequency produces a new method to detect the onset of pilot-induced oscillations. This paper will further describe system identification tools that extract modal information of aeroelastic vibrations observed in flight. Because it is often difficult to obtain input excitation data, particularly in real time, Systems Technology, Inc. developed a modal identification software toolbox that provides an innovative approach based on curve-fitting frequency domain decomposition, which relies only on output sensor data to identify the aeroelastic modes. Flight-test data are used to demonstrate the effectiveness and efficacy of the system identification approaches.

Direct Numerical Simulations of Turbulent Flow over Low-Pressure Turbine Blades with Aeroelastic Vibrations and Inflow Wakes

In the present work, direct numerical simulation is employed to investigate the unsteady flow characteristics and energy performance of low-pressure turbines (LPT) by considering the blades aeroelastic vibrations and inflow wakes. The effects of inflow disturbance (0 < φ < 0.91) and reduced blade vibration (0 < f < 250 Hz) on the turbulent flow behavior of LPTs are investigated for the first time. The transient governing equations on the vibrating blades are modelled by the high-order spectral/hp element method. The results revealed that by increasing the inflow disturbances, the separated bubbles tend to shrink, which has a noticeable influence on the pressure in the downstream region. The maximum wake loss value is reduced by 16.4% by increasing the φ from 0.31 to 0.91. The flow separation is majorly affected by inflow wakes and blade vibrations. The results revealed that the maximum pressure coefficient in the separated flow region of the vibrating blade has been increased by 108% by raising φ from 0 to 0.91. The blade vibration further intensifies the vortex generation process, adding more energy to the flow and the downstream vortex shedding. The vortex generation and shedding are intensified on the vibrating blade compared to the non-vibrating one that is subject to inflow wakes. The results and findings from this paper are also useful for the design and modeling of turbine blades that are prone to aeroelastic instabilities, such as large offshore wind turbine blades.

A graphical method for the analysis of the aeroelastic crosswind vibrations of a square cylinder

This paper proposes a simple and fast method to obtain the aeroelastic response of a square cylinder following different modelling approaches underpinned by a novel graphical technique that establishes abstract relationships between different key physical parameters involved in the mathematical models. The method is applied to the analysis of three important aeroelastic problems in the crosswind response of a square cylinder, including the transverse galloping defined with a quasi-steady model, the vortex-induced vibration (VIV) using a nonlinear oscillator model, and the VIV-galloping interaction following a combined effects model. The results demonstrate that the proposed analytical method simplifies the analysis and it is able to capture most of the complex aeroelastic crosswind behaviors of a square bluff body.

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.

Modeling of aeroelastic composite plates vibrations based on asymptotic theory

The paper is devoted to solving the problem of aeroelastic deformation of multilayer thin composite plates. A theory of aeroelastic deformations of composite plates based on the application of the asymptotic averaging method and piston theory for modeling pressure on the body surface is proposed. The averaged equations of aeroelastic vibrations of composite plates are derived. An example of a numerical solution of the problem of one-dimensional bending vibrations of a composite plate based on the developed theory is given.

Enhanced performance of airfoil-based piezoelectric energy harvester under coupled flutter and vortex-induced vibration

This paper designs a novel airfoil-based flutter piezoelectric energy harvester attached to an unconstrained trailing-edge flap, for transforming the vibration mode and improving the harvesting performance. The flap is first constrained by the flap spring rod and takes place the torsion motion at the smaller angle around the flap shaft. While, when the flap spring rod is removed, the flap is unconstrained, rotates freely, and results in transforming the vibration mode. The mathematical model of fluid-structure-electric coupled fields of the harvester system is first derived, the simulation model of the multi-physical coupled fields is then built, and the wind tunnel experimental setup is finally fabricated. The influence of the flap motions and structural parameters on the flow field, vibration characteristic, and harvesting performance are investigated theoretically, numerically, and experimentally. The results demonstrate that the vibration mode of the harvester system transforms from flutter to vortex-induced vibration at the smaller flap damping coefficients. The flow field verifies that the vortices are shedding at the trailing-edge of the flap and the vibration mode transformation occurs. The unconstrained flap first takes place flutter and then vortex-induced vibration with the increase of the airflow velocity, which enhances the harvesting performance. The unconstrained flap, pitch free play, and the smaller plunge stiffness coefficient decrease the flutter onset of velocity, enhance the aeroelastic vibration and thus improve the harvesting performance. A maximum plunge amplitude of 0.077 m, output voltage of 36.83 V, and output power of 5.43 mW can be harvested for the harvester system “Unconstraint and 1 mm” at 14.39 m/s and 278 N/m. The maximum enhancement ratio of output power for “Unconstraint and 1 mm” is 727.4% higher than that for “Constraint and Zero”. The designed harvester can directly power 14 LEDs and indirectly power a LED for 5 s. This research provides an essential foundation for designing more efficient piezoelectric energy harvesters for promoting actual utilizations in the low-power wireless sensor system.

Stochastic aeroservoelastic analysis of a flapped airfoil

In order to increase the operability range of wings in terms of speed, the suppression of aeroelastic vibrations due to flutter phenomena using a trailing edge flap is analyzed. The aeroelastic modelling of a three degrees of freedom 3DOF airfoil in unsteady incompressible flow with pitch and control surface stiffness non-linearities is studied and an augmented state space representation is used for the time domain analysis of the problem. A V-stack piezoelectric actuator is used to move the trailing edge flap and its dynamic behavior is included in the analyses by means of a finite element model; the actuator input voltage saturation is also taken into account. A heuristic method, named Population Decline Swarm Optimization, is used for the tuning of the filtered PID controller parameters for different velocity values. The optimization algorithm is also used for the tuning of the Simple Adaptive Controller SAC invariant gains. A general uncertain state space modelling of the aero-servo-elastic plant is provided and used first for the open loop stochastic flutter analysis. Then, the stochastic robustness analysis is carried out to verify the robustness to structural, aerodynamic, and actuator parameters uncertainties of the proposed flutter suppression systems and to compare the gain scheduled PID approach with the SAC scheme.

Scavenging energy from aeroelastic vibrations for hybrid stall control in a fixed-wing micro aerial vehicle

Scavenging energy from aeroelastic vibrations was considered for a self-powered hybrid passive-active stall control system intended to improve the aerodynamic performance of fixed-wing micro aerial vehicles without exhausting available batteries. It was found that the passive component of the system generates intense streamwise vortices, which give rise to vortex-induced vibrations. Measured frequency response functions indicated accelerations in a wing prototype up to 0.1 g at relatively low frequencies, when it was operated at simulated flight conditions in a wind tunnel. Aiming to use this resource for additional power, a piezoelectric energy harvesting device was installed inside the wing and tuned for resonant response. Two electromechanical modeling approaches for the piezoelectric harvester were investigated, namely, an analytical model and finite elements simulations. A comparison with experimental results has shown that the latter approach is better equipped to deal with advanced designs, yielding accurate predictions in the present study. Extracted power and generated voltage were quantified as a function of the electric loading resistance. The reported data demonstrated that the proof of concept was achieved, so that a lightweight, low-consumption actuator for the active component of the stall control system can be powered by the energy of structural vibrations.

Comprehensive Engineering Frequency Domain Analysis and Vibration Suppression of Flexible Aircraft Based on Active Disturbance Rejection Controller.

The crash of an aircraft with an almost vertical attitude in Wuzhou, Guangxi, China, on 21 March 2022, has caused a robust discussion in the civil aviation community. We propose an active disturbance rejection controller (ADRC) for suppressing aeroelastic vibrations of a flexible aircraft at the simulation level. The ADRC has a relatively simple structure and it has been proved in several fields to provide better control than the classical proportional-integral-derivative (PID) control theory and is easier to translate from theory to practice compared with other modern control theories. In this paper, the vibration model of the flexible aircraft was built, based on the first elastic vibration mode of the aircraft. In addition, the principle of ADRC is explained in detail, a second-order ADRC was designed to control the vibration model, and the system’s closed-loop frequency domain characteristics, tracking effect and sensitivity were comprehensively analyzed. The estimation error of the extended state observer (ESO) and the anti-disturbance effect were analyzed, while the robustness of the closed-loop system was verified using the Monte Carlo method, which was used for the first time in this field. Simulation results showed that the ADRC suppressed aircraft elastic vibration better than PID controllers and that the closed-loop system was robust in the face of dynamic parameters.

Simple adaptive V-stack piezoelectric based airfoil flutter suppression system

The suppression of aeroelastic vibrations due to flutter using a trailing edge flap is analyzed to increase the speed operability range of wings. The aeroelastic model of a 3DOF airfoil in incompressible flow is presented and an augmented state-space representation is used for the time domain analysis. A finite element model of a V-stack piezoelectric actuator, used to move the trailing edge flap, is introduced to model the actuator dynamics. The use of the simple adaptive controller is investigated to realize an adaptive flutter suppression system. A parallel feedforward compensator is tuned to make the plant almost strictly passive and a metaheuristic algorithm is used to determine the invariant parameters. Numerical simulations are carried out to verify the performance of the simple adaptive flutter suppression system in presence of speed variations and disturbances. Numerical results proved that the SAC flutter suppression system improves the closed loop system flutter boundary with respect to a gain scheduled PID controller.

Exploration of an unconventional validation tool to investigate aero engine transonic fan flutter signature

Abstract Flutter, an aeroelastic blade vibration phenomena, experienced by the fan of an developmental aero gas turbine engine, result in blade failure. Hence, suitable flutter detection instrumentation is required during engine testing. Flutter signature capture from revolving blades is a challenging task that necessitates either a complicated strain gauge-based rotating instrumentation or a noncontact tip timing system. Authors investigated a unique way for identifying, measuring, and validating flutter signature by assessing wall static pressure pulsations produced during blade tip transit across a casing mounted high bandwidth sensor during this research. The authors devised a mathematical model to explain signal spectrum components that feature both amplitude and angle modulation properties at the same time. The theory was tested using first-stage fan rotor blades that were fluttering in the first flexural mode (1F) and forming the second nodal diameter (2ND). The approach’s estimated blade deflection was compared to measurements taken using a traditional tip timing method up to 7 mm and determined to be within 1% inaccuracy. This research provides a low-cost, easy alternative technique for measuring flutter during engine development testing.