Flutter Characteristics Research Articles

Uncertainty analysis of rudder shaft thermal conditions on the flutter characteristics of the hypersonic control surface

The thermal conditions in hypersonic aerothermoelastic systems exert a significant influence on the flutter characteristics of the system. Nevertheless, in previous investigations on aeroelastic uncertainty analysis, the influence of thermal uncertainty has frequently been neglected. In this study, an uncertainty analysis framework based on Monte Carlo simulation and surrogate model is conducted for addressing the thermal uncertainty and its implications on the flutter characteristics. Initially, the all-moving control surface of a hypersonic vehicle is selected as the investigated model. A parametric method is then developed to represent the temperature distribution along the control rudder shaft, taking into account the temperature conditions calculated by CFD. Based on the approach, the impact of temperature uncertainty is designed to perform the uncertainty quantification of temperature uncertainty on flutter characteristics of the control surface. Sensitivity indices are computed to evaluate the impact of temperature uncertainty in different regions of the shaft on flutter characteristics. This implies BPNN always provides accurate models. This is not always true and even if it is, showing that in a general sense is not within the scope of this study. Furthermore, the temperature uncertainty on the shaft surface induces uncertainty in the modal frequencies of the control surface, thereby resulting in uncertain flutter characteristics. Notably, the leading-edge region of the shaft exhibits the most pronounced effect on flutter characteristics, followed by the midsection region. These results could offer valuable insights for the refined design of control surfaces in hypersonic vehicles, contributing to the advancement of this field of research.

The effect of aspect ratio and mass ratio on the flow-induced flutter of a thin flexible sheet

This study experimentally investigates the flow-induced flutter of a thin flexible sheet, focusing on how the sheet's aspect ratio and mass ratio affect its stability and flutter characteristics in the post-critical regime. The flutter frequency of the sheet was obtained using hotwire measurements, while flutter amplitude and mode shape were acquired through high-speed imaging. The flowfield around the flapping sheet was analyzed using particle image velocimetry (PIV). Based on experimental observations, we report the onset of flutter as a subcritical bifurcation with hysteresis. The dynamic characteristics of the sheet play a significant role in its flutter instability, with the onset and cessation of flutter occurring at a frequency close to the sheet's second-mode natural frequency. The results show that both aspect ratio and mass ratio significantly affect the critical wind speed and flutter characteristics in the post-critical regime. Both flutter frequency and amplitude decrease as the aspect ratio decreases. PIV measurements in various planes reveal the highly three-dimensional nature of the flow. Results from off-axis PIV show a pair of counter-rotating spiral vortices in the wake that oscillate and change orientation with the sheet's movement. Additionally, a theoretical analysis was conducted to derive an approximate analytical relationship between the aspect ratio and critical wind speed. Experimental results aligned well with theoretical predictions for sheets with low aspect ratios (aspect ratio ≤1) but deviated for sheets with higher aspect ratios (aspect ratio >1). The relevant scaling parameters have also been explored to represent the experimental data in a non-dimensional form.

Numerical investigation on transonic flutter characteristics of an airfoil with split drag rudder

In this paper, a series of flutter simulations are carried out to investigate the effects of split drag rudder (SDR) on the transonic flutter characteristic of rigid NACA 64A010. A structural dynamic model addressing two-degree-of-freedom pitch-plunge aeroelastic oscillations was coupled with the unsteady Reynolds-averaged Navier-Stokes equations to perform flutter simulation. Meanwhile, the influence mechanism of SDR on flutter boundary is explained through aerodynamic work and the correlated shock wave location. The results show that the SDR delays the shock wave shifting downstream, and the Mach number corresponding to reaching freeze region increases as the split angle increases. Therefore, the peak value of aerodynamic moment coefficient amplitude and the sharp ascent process of phase occurs at higher Mach number, which leads to the delay in the occurrence of the transonic dip. Besides, before the transonic dip of airfoil without SDR occurs, the aerodynamic moment phase of airfoil with the SDR decreases slowly due to the decrease in the speed of shock wave moving downstream. This results in an increased flutter speed when employing the SDR before the transonic dip of airfoil without SDR occurs. Meanwhile, the effects of asymmetric split angles on the transonic flutter characteristics are also investigated. Before the transonic dip of airfoil without SDR occurs, the flutter characteristic is dominated by the smaller split angle.

Isogeometric flutter analysis of a heated laminated plate with and without cutout

Understanding the flutter characteristics of heated laminated plates, both with and without cutout, is crucial. This study presents the first exploration of flutter analysis in a thermal environment for a laminated plate featuring a cutout. To facilitate this study, the motion equations of the heated laminated plate with a cutout are derived using the first-order shear deformation theory (FSDT), incorporating a nonlinear term. Employing the isogeometric method combined with multi-path coupling technology, we establish accurate geometric and solution domains for the laminated plate. The effects of the thermal stresses and the aerodynamics calculated by the linear piston theory are considered. The accuracy and effectiveness of the proposed model are validated through several comparisons with ANSYS results and existing solutions. Additionally, the study examines the impact of key parameters on flutter characteristics, including thermal conditions, number of layers, lay-up angles, inflow angles, and cutout dimensions. The insights gained from this research will serve as a valuable benchmark for future analyses and design concerning flutter characteristics.

Research on the flutter characteristics of folding wings with variable swept angles of the outer wing

The critical flutter speed, along with the associated stability and safety of a folding-wing aircraft, has been evaluated for variable wing configurations based on traditional designs. Through theoretical analysis and numerical simulation validation, the contributions of parameters such as the hinge stiffness, sweep angle, and folding angle on the flutter and stability of the folding wing are investigated in detail. It is observed that under a specified safe hinge stiffness, the proposed variable-sweep folding-wing configuration can enhance the critical flutter speed at a dangerous folding angle. Through the joint manipulation of the folding and sweep angles, the aerodynamic drag of the folding wing was reduced, thereby enhancing its flight speed and flutter boundaries. This paper aims to provide novel insights into the design and stability analysis of variable-wing configurations.

Analysis of aerodynamic characteristics of drone wing based on CFD

In order to improve the aerodynamic characteristics of the drone wings, CFD method was used to simulate and calculate the lift coefficient, drag coefficient, and lift-drag ratio under different relative inflow velocities, as well as the velocity and pressure fields under different attack angles. Modal calculations were conducted on the wing to obtain the first four modal shapes, providing a basis for analyzing flutter characteristics. An iterative calculation method of incompressible potential flow-boundary layer based on surface element method was combined with the software XFOIL to optimize the airfoil at low wind speeds. The results indicate that the airfoil is susceptible to stall at high angles of attack, with the pressure of the separation flow being nearly equivalent to that at the separation point. Subsequent to separation, there is an increase in differential pressure resistance, resulting in a marked rise in the drag coefficient. At the optimized angle of attack, the lift-drag ratio of the optimized wing increases by 12.58 %, while there is a decrease of 0.084 % in lift coefficient and an increase of 11.21 % in drag coefficient.

Flutter Mechanism of a Thin Plate Considering Attack Angles

It is well known that the flutter performance of a section is sensitive to the changing wind angles of attack. Exploring the thin plate’s flutter mechanism under different angles of attack is excellent, which helps understand inner flutter characteristics and ensures structural safety. This study investigated flutter derivatives of a thin plate with an aspect ratio of 40 under different wind angles of attack via the forced vibration technique. The otherness of aerodynamic damping and phase lag under different wind angles, which helps in understanding the flutter mechanism, are analyzed using the bimodal-coupled flutter method. It is shown that coupled vertical–torsional flutter dominated the flutter modality under 0° and 3° wind angles of attack. The critical flutter velocity dramatically decreased with increasing wind angles of attack which is attributed to the increasing negative aerodynamic damping induced by coupled self-excited forces and the decreasing positive aerodynamic damping induced by uncoupled self-excited forces. Moreover, the vertical motion lags behind the torsional motion under the 7° angle of attack, which was totally contrary to other angles of attack. Major works in this study reveal the aerodynamic mechanism of the weakened flutter performance of thin plates under large wind angles of attack and provide a reference for the flutter analysis of thin plates.

A Study on Post-Flutter Characteristics of a Large-Span Double-Deck Steel Truss Main Girder Suspension Bridge

To investigate the nonlinear flutter characteristics of long-span suspension bridges under different deck ancillary structures and configurations, including those with and without a central wind-permeable zone, as well as to analyze the hysteresis phenomenon of a subcritical flutter and elucidate the mechanisms leading to the occurrence of nonlinear flutter, this paper studies first the post-flutter characteristics of the torsion single-degree-of-freedom (SDOF) test systems and vertical bending–torsion two-degree-of-freedom (2DOF) test systems under different aerodynamic shape conditions are further analyzed, and the role of the vertical vibration in coupled nonlinear flutter is discussed. The results indicate that better flutter performance is achieved in the absence of bridge deck auxiliary structures with a central wind-permeable zone. The participation of vertical vibrations in the post-flutter vibration increases with the increase in wind speed, reducing the flutter performance of the main girder. Furthermore, the hysteresis phenomenon in the subcritical flutter state is observed in the wind tunnel experiment, and its evolution law and mechanism are discussed from the perspective of amplitude-dependent damping. Finally, the vibration-generating mechanism of the limit oscillation ring is elaborated in terms of the evolution law of the post-flutter vibration damping.

Investigation on nonlinear flutter modes competition of a long-span suspension bridge based on full-bridge aeroelastic model tests

Nonlinear flutter has attracted wide attention due to the bottleneck caused by linear flutter theory on flutter-resistant design of super-long-span bridges. The longer the span, the more closely spaced the natural modes, which may cause competition among flutter-modes in a nonlinear flutter, but it is rarely reported so far. To this end, this study experimentally investigates the 3D nonlinear flutter characteristics of a long-span suspension bridge with closely spaced natural modes based on full-bridge aeroelastic model wind tunnel tests. Since there are two unstable flutter-modes within the interested post-critical regime and thus various complex but interesting flutter-modes competition processes were observed, such as continuous modes competition where the vibration amplitude evolution exhibits various different types of “sawtooth” shapes during stable vibration stages. Meanwhile, the complex nonlinear bifurcation behaviors caused by modes competition were also observed. The evolutionary characteristics of flutter-modes competition are analyzed in detail and relevant mechanisms are discussed. As the wind speed increases, the flutter of the studied bridge mainly undergoes a transition from being dominated by the symmetric mode to being dominated by the antisymmetric mode, accompanied by a continuous modes competition zone in between as a transitional zone. The results show that the continuous modes competition will result in a decrease in the maximum amplitude RMS of the full-span, which is beneficial for the structure. But it may also lead to a transient increase in the maximum amplitude of the full-span due to the coupling vibration shape formed by the two significant flutter-modes, which may be bad for the structure.

CONCEPTUAL ANALYSIS ON THE IMPACT OF ACOUSTIC LINERS IN FAN FLUTTER

Abstract This work investigates the impact of acoustically treated intakes on fan flutter. The propagation of the fan acoustic perturbations is studied using a simplified model, where the frequency of the waves in the intake is the natural frequency of the fan blade in the stationary frame of reference. The model consists of a constant cross-section annular duct, where the acoustic modes are computed for hard wall and lined wall regions, assuming a uniform axial flow. The interfaces between the lined and hard wall sections are solved by doing mode matching. The acoustic reflections in the zero-thickness intake are computed using the Wiener-Hopf technique following Rienstra's model. Analytical results show that the waves propagating from the fan are reflected and scattered radially at the interfaces between the hard wall and the liner. Furthermore, the liner damps and changes the phase velocity of acoustic modes. Due to the low frequency of the flutter waves, the radial scattering can activate different cut-off modes, which need to be retained in order to make accurate predictions. The likelihood of fan flutter is estimated using the phase of the reflected cut-on waves reaching the fan. This strategy is used to assess the impact of the acoustic liners on the stability of a realistic fan. It is concluded that the impact of the phasing and reflections induced by the acoustic liners is comparable to that of the intake and can alter the flutter characteristics of the fan significantly.

Aerodynamic and flutter performance of the bridge deck with various countermeasures using computational fluid dynamics

Aerodynamic layouts of bridge decks considerably affect aerostatic torsional divergence and flutter for bridges. The crucial operation is choosing the optimal bridge deck shape considering the aerodynamic effect. The present study intends to provide a better solution for the flutter control scheme by changing five aspect ratios and four passive aerodynamic countermeasures. The countermeasures are an eccentric wing, inspection rail, down vertical central stabilizer and wind barrier, which have been used for three deck shapes: streamlined, semi-streamline and bluff body sections with large angles of attack. Nowadays, wind barriers are frequently installed on bridges to shield vehicles from the harmful effects of crosswinds, which can influence the flutter characteristics of the bridge. Therefore, the present study contemplates reducing the flutter effect with countermeasures. These countermeasures adversely affect the deck’s dynamic stability, mainly manifested in the different divergence forms of the structure. Finally, the eccentric wing, which runs parallel to the bridge deck, increases the critical flutter speed. However, the flow that passes through the eccentric wing extracts considerable energy from the flow field of the countermeasure. Therefore, the framework and solution of the present investigation are sustainable and safe for bridge design.

Study on Nonlinear Flutter Characteristics of Single-Box Section and Twin-Box Section as a Three-Degree-of-Freedom System

The accurate prediction of the nonlinear flutter response is one of the important prerequisites for accurately evaluating the post-flutter performance of long-span bridges. In fact, as the vibration amplitude increases, the participation of lateral degree-of-freedom (DOF) will become more and more obvious and thus ignoring self-excited forces related to lateral vibration may no longer be applicable. To this end, based on 18 amplitude-dependent flutter derivatives (FDs), a 3-DOFs coupled nonlinear flutter analysis method was proposed in this study. Then, 18 amplitude-dependent FDs of two typical bridge decks were identified, and they were used to calculate the 3-DOF coupled nonlinear flutter responses based on the proposed flutter analysis method. Meanwhile, the correctness of the above flutter analysis method was also verified by compared with the numerical simulation results. Finally, the influence and mechanism of the lateral DOF, structural modal parameters and amplitude-dependent FDs on the nonlinear flutter of these typical bridge decks were investigated. The results show that when the torsional amplitude of the nonlinear flutter is large, the participation of lateral DOF will significantly increase the steady-state amplitude of the nonlinear flutter, and the larger the torsional amplitude, the more significant this increase is. The main reason is the participation of the lateral DOF introduces the negative coupled aerodynamic damping to the system, which then reduces the stability of the system. Besides, for the twin-box section, the influence of the lateral DOF on the nonlinear flutter is relatively smaller compared with the single-box section since the proportion of negative aerodynamic damping by the lateral DOF is smaller. Compared with the single-box section, the mass of the twin-box section has a smaller effect on the critical wind speed, and the torsional structural damping ratio of the twin-box section has a greater effect on the nonlinear flutter.

Dynamic modeling and active aeroelastic flutter control of functionally graded irregular plates with piezoelectric layers based on the discrete-coupling method

The research on active flutter control of functionally graded material structures is of great significance to improve the safety and stability of aerospace systems. Therefore, the purpose of this study is to analyze the active flutter control of functionally graded irregular plates (FGIP) by attaching piezoelectric layers to their surfaces. Firstly, a discrete-coupled modeling method for irregular panel structures is proposed. The main modeling idea is to discretize the whole structure and calculate the energy expression of the discretized individuals. Then, the adjacent individuals are coupled by artificial springs. Finally, the dynamic model of irregular panel structure is established based on the Hamilton principle. The validity of this modeling method is verified by comparing the results with the natural characteristics of the finite element model. The first-order supersonic piston theory is used to calculate aerodynamic pressure, and the flutter characteristics of FGIP under supersonic airflow are analyzed. In addition, the influence of the power law index of functionally graded materials on structural flutter characteristics is discussed. To suppress the flutter of FGIP, the displacement feedback control method is used to provide active stiffness for the structure and then change the flutter characteristics of the structure. The results show that active control can effectively improve the anti-flutter ability of the structure.

Modeling of nonlinear self-excited forces: A study on flutter characteristics and mechanisms of post-flutter behaviors

The intrinsic physical relevance of higher-order self-excited force (SEF) components has received limited attention, and there is a dearth of formulas that adequately analyze the influence of SEF components on the post-flutter characteristics. Based on Taylor formulas and the principle of independence, semi-empirical polynomial SEF models are developed and validated. The energy input efficiency and role of each order SEF component are examined using the proposed models. By introducing the principle of energy equivalence and approximate average power, theoretical formulas designed to calculate the post-flutter characteristics are established. Finally, the applicability and robustness of the SEF models and theoretical formulas are discussed. Results show that the proposed models can obtain independent higher-order SEF components, which is conducive to the correct analysis of the SEF driving mechanisms. The theoretical formulas can accurately reconstruct the time-varying curves of the flutter characteristics, and the terms in the formulas can explicitly calculate and analyze the mechanism of each SEF model element. It is observed that the higher-order SEF components have a significant impact on the accurate reconstruction of SEFs while barely affecting the system energy. Moreover, the limit cycle oscillation generation mechanisms of the investigated two rectangular cylinders are different, but the variation of the flutter characteristics with time remain the same.

Effect of nonlinear terms in piston theory on characteristics of panel flutter

Currently, there is no systematic summary of the influence of the nonlinear terms in piston theory on the panel flutter. The two-dimensional nonlinear panel flutter equations under supersonic airflow based on the first, second, and third-order piston theories is established. The stability of the heated panel is analyzed by using the Lyapunov's indirect method, and the panel flutter equations are numerically solved based on the numerical analysis method to investigate the influence of the nonlinear terms in piston theory on the panel flutter. The results show that: ①Under a small temperature rise ratio, the panel response under the first-order piston theory only exhibits the convergent motion and single-period limit cycle flutter. While under higher-order piston theories, the panel response is more complex, exhibiting more complex nonlinear dynamic phenomena such as multi-period limit cycle flutter and chaotic motion in addition to the aforementioned characteristics. ②As the Mach number increases, the required dynamic pressure and temperature rise ratio decrease gradually when the dynamic response of the panel under the first-order piston theory and higher-order piston theories exhibit significant differences. ③The significant differences in the computational results of the second-order and third-order piston theory appear under the high Mach numbers and relatively high dynamic pressures, and the same phenomenon occurs underthe high temperature rise ratios. ④When the dynamic response characteristics of the panel are basically consistent, the displacement response peak calculated by using the higher-order piston theory is usually smaller than the result calculated by using the first-order piston theory, and the maximum error can reach about 16.66%. The present results have certain reference value for selecting the appropriate analysis method for the panel flutter under different conditions in practical applications.

Nonlinear thermal flutter of variable angle tow composite laminates in supersonic airflow

Compared with traditional composite materials, variable stiffness composite materials with curvilinear fiber paths have higher design flexibility and the potential to improve structural efficiency. In view of this, the nonlinear flutter characteristics of Variable Angle Tow (VAT) composite laminates with thermal effect in supersonic airflow are investigated in this paper. The proposed panel flutter model is developed based on the von Kármán large deformation plate theory. The thermal stress is approximated according to the quasi-steady thermal stress theory, whilst the aerodynamic pressure is calculated based on the first-order piston theory. The aerothermoelastic equations of motion are first established using Hamilton’s variational principle, and the Rayleigh-Ritz method is then applied to solve the governing equations in the space domain. The time-domain nonlinear equations are solved through the fourth-order Runge-Kutta method. The accuracy and convergence of the proposed method are verified through the comparisons with the results available in the literature. The effects of several parameters such as fiber orientation angle, thermal load, and aerodynamic pressure on the nonlinear flutter responses of VAT laminates are comprehensively discussed. Several dynamic behaviors of VAT laminates, including stable flat, buckled, Limit Cycle Oscillation (LCO), multi-periodic motion, quasi-periodic motion, and chaotic motion, are revealed by using the time history, phase portrait, Poincaré map, and bifurcation diagram. The results presented herein may be beneficial for the design of VAT laminates in supersonic airflow.

Study on coupled mode flutter parameters of large wind turbine blades

As the size of wind turbine blades increases, the flexibility of the blades increases. In actual operation, airflow flow can cause aerodynamic elastic instability of the blade structure. Long blades may experience coupled mode flutter due to the bending torsion coupling effect, leading to blade failure. Based on Euler Bernoulli beam theory combined with Theodorsen non directional aerodynamic loads, a blade flutter characteristic equation is established through finite element method. Taking NREL 5 MW wind turbine blades as an example, analyze the influence of parameter changes in different regions of the blades on flutter characteristics. Research has found that paramter changes in the tip region of blade have the greatest impact on flutter characteristics. The vibration frequency shows an overall upward trend with the increase of waving stiffness and torsional stiffness. The flutter velocity of the three regions tends to stabilize as the bending stiffness decreases. The blade flutter speed increases with the increase of torsional stiffness. The radius of gyration is inversely proportional to the flutter frequency and flutter velocity. The impact of centroid offset on blade structure flutter frequency is minimal, but the centroid offset in the tip region has a greater impact on flutter velocity. Increasing the torsional frequency can prevent coupled mode flutter and provide a theoretical basis for blade flutter prevention design.

Flutter Characteristics of a Modified Z-Shaped Folding Wing Using a New Non-Intrusive Model

Unmanned aerial vehicles (UAVs) with folding wings can serve in multiple mission profiles, usually accompanied by sudden changes in flight speed. These bring great challenges to the aeroelastic design of UAVs, especially in the calculation of flutter characteristics. This paper developed a new non-intrusive aeroelastic model to quickly calculate the flutter characteristics of Z-shaped folding wings at different folding angles. First, the original Z-shaped folding wing was designed to be enhanced. Beams and ribs were arranged inside each wing segment to enhance the structural strength performance. Control surfaces were arranged in the middle-wing and outer-wing to enhance the aerodynamic control performance. Second, a parametric aeroelastic model at any folding angle was reconstructed based on the input file of Nastran software for the flutter calculation of the folding wing in the unfolded state. Finally, the effects of parameters such as folding angle, hinge stiffness between different wing segments, and hinge stiffness of the control surfaces on the flutter characteristics of the folding wing were investigated. The results show that the enhancement scheme could significantly increase the flutter speed and flutter frequency of the folding wing. The hinge stiffness between each wing segment had a significant impact on the flutter characteristics of the folding wing, but flutter at the control surface basically did not occur.

Aeroelastic-electric flutter characteristics of functionally graded piezoelectric material plates in supersonic airflow

Aeroelastic-electric flutter characteristics of functionally graded piezoelectric material plates in supersonic airflow

Flutter characteristics of a sheet with an elastic support in three-dimensional uniform flow

In the manufacturing processes of thin flexible plates (sheets) such as polarizing films, the flutter can be caused to the sheets due to the interaction between the motion of the sheets and fluid flow. Then, the flutter can cause serious damage to the sheets, leading to the wrinkles and scratches. Thus, it is crucial to investigate a detailed characteristics and excitation mechanism of the flutter. In the present study, a detailed flutter characteristics and excitation mechanism of a rectangular sheet with an elastic support is investigated. The elastic support is implemented using a fine flexible wire. The influence of bending stiffness of the support section on the flutter velocity and frequency is clarified through wind-tunnel experiments and numerical analysis. Moreover, the work done by the fluid force on the sheet surface was determined.The flutter velocity and frequency drastically decrease owing to decrease in bending stiffness of the support section regardless of the aspect and mass ratio. Then, the positive work region around the leading edge of the sheet expands owing to the large-amplitude oscillation around the leading edge. The expansion of positive work region owing to a large-amplitude oscillation around the leading edge of the sheet destabilizes the system.