Flutter Analysis Research Articles

Flutter in a simplified blade cascade: Limits of the quasi-steady approximation

Flow-induced vibration in turbomachinery represents a major and persistent concern, especially in modern turbine and compressor designs with long and slender blades operating in transonic flow conditions. There is a wide range of computational and experimental methods for blade flutter prediction and analysis. In certain situations, the quasi-steady approximation can be utilized, considering the unsteady flow as a sequence of steady flow fields for each position of the oscillation cycle. The study is focused on experimental investigation of the limits of applicability of the quasisteady approximation in the case of a simplified linear five-blade cascade with the middle blade undergoing high-frequency torsional oscillation due to kinematic excitation. A measurement campaign of more than 100 wind tunnel runs was carried out for flow velocities ranging from high subsonic to transonic regimes (M = 0, 0.529, 0.777 and 1.018), frequency ratios 0 - 0.75 and reduced frequencies k = 0 – 0.41. A comparison of quasi-steady and time-resolved blade surface pressure measurements is reported, and the degree of unsteadiness of the airflow is quantified. For low reduced frequencies the stationary distributions match almost perfectly the time-resolved profiles. The degree of unsteadiness remains below 2% up to k = 0.1 for the subsonic and supercritical flow regimes. For reduced frequencies above 0.2, the global degree of unsteadiness increases quickly up to 10%, with local differences between the stationary and time-resolved pressure profiles up to 40%. In the case of transonic flow regime, the flow unsteadiness is generally higher and further complicated by intermittency — stochastic transition from supersonic to subsonic flow in the aft part of the blade.

Techniques for adjusting qualities of aircraft structural models for more effective aeroelastic flutter analyses

To solve numerically the problem of aeroelastic flutter, two virtual components are required: a structural finite element model (FEM) and an aerodynamic model. MSC Software package containing Nastran with embedded flutter solution enables to perform calculations with the use of an integrated aeroelastic model. For data block including the model and the set of entry parameters, flutter equation is being solved. On the basis of postprocessed output data curves of run for resulting parameters can be plotted which gives information of flutter critical point.Numerical results may be subject to some uncertainty. Result deviation could occur as effects of various factors resulting from inaccurate geometry or poor structural qualities of mapped aircraft. Structural defects affecting mass or stiffness matrices of FEM are often hard to identify. Aspects important for effective flutter solutions are strictly connected with the coincidence of structural properties of the real aircraft and its model. In the paper, the method of numerical flutter analysis was presented with the use of techniques available in MSC Nastran. Three assessment methods were proposed to identify structural parameters usable for validating FEMs. The method of mass correction relies on adjustment of model mass values and tuning the location of the center of mass of the model to the coordinates of the location of the center of mass of the real aircraft. For adjusting stiffness of model parts, very useful are results obtained from strength test of the real airframe. The completely reliable but costly method is performing ground vibration tests (GVT) to measure precisely resonant frequencies and natural modes of free vibrations. The results obtained from experiments should be treated as the referenced, but tuning FEM to them requires both adjusting numerical eigenfrequencies and normal modes.

Identification of the High-Order Rational Function of Bridge Decks by SDOF Forced Vibration Testing

The high-order rational function provides an accurate and effective model of self-excited forces for flutter analysis of bridges. This study proposes a direct identification method for the rational function of a bridge deck, which enables high-order modeling. In this method, the single degree of freedom (SDOF) forced vibration test is first carried out on the sectional model of the bridge deck. The tested results are then processed by a harmonic function-based filter, yielding force time histories with high signal-to-noise ratios. Formulas are derived to identify parameters of the high-order rational function from these time histories. To deal with the numerical difficulties of the formulas, two practical optimal nonlinear fitting procedures were proposed, which simplify the identification but at the same time maintain a reasonable accuracy. A thin flat plate and a streamlined box section under various wind angles of attack were used as examples to elucidate the effectiveness and feasibility of the proposed identification method. Results showed that the identified high-order rational function could accurately replicate the self-excited force. In contrast, a significant deviation was observed if the first-order rational function was utilized as an alternative. Finally, the high-order rational function model identified was applied in the flutter analysis by a state-space method. The yielded critical flutter wind speed matched satisfactorily with the free-vibration wind tunnel test results, confirming the advantage of the proposed model.

Advancement of Aerodynamics in Flutter Characteristics of AGARD 445.6 Wing

Abstract: The aerospace sector has seen a significant prominence in the field of aerodynamics. Aerodynamic behaviour differs from one structure to the next depending on the specifics of each one. Due to flexible aeroplane structures, aeroelastic phenomena occur, when structural deformations alter aerodynamic forces. A feedback mechanism between the increased structural deformations and the added aerodynamic forces increases further aerodynamic loads. These interactions may diminish until they achieve an equilibrium state or, if resonance takes place, they may diverge drastically. The most challenging to forecast instability aeroelasticity aeroelastic phenomenon is flutter. An accurate finite element aerodynamic wing model is required for flutter study. A review of various approaches for conducting flutter analysis of AGARD 445.6 wing is presented in this paper. AGARD 445.6 wing has been used as standard configuration for the analogy of all aeroelastic behaviours. Under different flow regimes, the paper examines the platforms for finite element software that are used for flutter analysis.

Preliminary Flutter Stability Assessment of the Double-Deck George Washington Bridge

We deal with the flutter analysis of the George Washington bridge, in both the single- and double-deck configurations of 1931 and 1962, respectively. The influence of the additional lower deck on the aerodynamic behavior is investigated. To overcome the lack of aerodynamic data, a simplified approach is followed based on Fung’s formulation, in which the flutter derivatives are expressed in terms of the real and imaginary parts of the Theodorsen function and of the steady-state aerodynamic coefficients of the deck cross-section. The latter are obtained by Computational Fluid Dynamics simulations conducted in ANSYS FLUENT, whereas the ANSYS Mechanical APDL finite element package is used to perform the flutter analyses. Two different methods for the application of the aeroelastic forces are employed for the double-deck configuration: (i) self-excited forces, based on flutter derivatives related to the whole cross-section, acting on the upper deck; and (ii) self-excited forces, based on flutter derivatives related to the single deck, simultaneously applied to the upper and lower decks. The obtained results are critically compared with theoretical predictions of simple formulas available from the literature; it is suggested that laboratory tests are needed since no experimental results seem to be available.

High-Fidelity Gradient-Based Wing Structural Optimization Including Geometrically Nonlinear Flutter Constraint

Lightweight high-aspect-ratio wings make aircraft more energy efficient thanks to their lower induced drag. Because such wings exhibit large deflections, design optimization based on linear flutter analysis of the wing undeformed shape is inadequate. To address this issue, we develop a framework for integrating a geometrically nonlinear flutter constraint, which considers in-flight deflections, into a high-fidelity gradient-based structural optimization. The wing mass and stress constraints are evaluated on a linear built-up (detailed) finite element model to capture realistic structural features. The geometrically nonlinear flutter constraint is based on a condensed low-order beam representation of the built-up finite element model, which captures the impact of in-flight deflections with tractable computational effort for optimization. The flutter constraint is differentiated with respect to the detailed structural model sizing variables using the adjoint method to enable large-scale optimizations. The framework is demonstrated by minimizing the mass of a wingbox model subject to the geometrically nonlinear flutter constraint along with stress and adjacency constraints. The geometrically nonlinear flutter constraint adds a penalty of up to 60% of the baseline mass due to the impact of in-flight deflections on the flutter onset speed and its mechanism. In contrast, a linear flutter constraint evaluated on the undeformed wing adds a mass penalty of only 10%. This methodology can help design energy-efficient aircraft with high-aspect-ratio wings, which require geometrically nonlinear flutter analyses early in the design cycle.

Flutter of carbon-based nanohybrid composite panels

Recently, carbon-based composite aerospace and mechanical structures have considerable attention due to their great material and mechanical properties. Carbon nanotubes (CNTs) or graphene platelets (GPLs) reinforcements for different matrices are common for the design of modern multilayer structures. In the present paper, the supersonic flutter of nanohybrid composite multilayer panels is examined and discussed. The nanohybrid multilayer panel is made of different technologically justified configurations of polymer layers reinforced by CNTs and GPLs The effective material properties of each CNTs and GPLs layer are determined according to two well-established homogenization techniques: the Mori–Tanaka scheme and the modified Halpin–Tsai model, respectively. Reddy’s third-order shear deformation theory is applied to avoid determining shear correction factors for different distributions of material properties. Hamilton’s principle and the first-order piston theory are applied to formulate aeroelastic coupled equations of motion of the panel. The numerical meshless method is employed to discretize dynamic equations and find generalized multi-parametric characteristic equations functionally dependent on the parameters of the structure with different boundary conditions. The accuracy of the obtained solution and results is examined by comparing the determined natural frequency and critical aerodynamic pressure with those obtained in previous studies. Then, a comprehensive parametric study is carried out to show the effects of hybridization of different distribution patterns of CNTs and GPLs, weight fractions, total layer number, and aspect ratio of hybrid composite panels on the flutter bounds. Results show that the present method provides a highly effective general numerical model for flutter analysis of hybrid nanocomposite panels with different boundary conditions for all thickness categories including thick plates. Moreover, an optimization nanoparticles distribution for the flutter of the nanohybrid composite panel has been obtained.

Vibration and flutter analysis of damaged composite plates under thermal environment and its passive control using piezoelectric patches

The internal flaws will largely affect the structural and aeroelastic characteristics of composite structures, especially at high thermal environments. The influence of thermal conditions on the passive control of vibration and flutter characteristics of damaged composite plates with piezoelectric patches is investigated in this work. The mathematical model is developed for the damaged composite plates with piezoelectric patches under thermal conditions by the finite element method. Internal flaws are incorporated in the composite plates based on the anisotropic damage modeling concept. Present finite element formulation is coded in the Matlab environment. The natural frequency, flutter velocity and flutter frequency values for damaged composite plates are obtained at different thermal conditions. Deterioration in the vibration and flutter characteristics are observed due to the presence of internal flaw in composite plates in the different thermal environments. PZT patches are bonded on the surface of the damaged composite plates subjected to the thermal environment and studies are carried out with different input voltages. Thus the improvement in the vibration and flutter characteristics of a damaged composite plate by employing PZT patches is presented for varying thermal conditions.

Research on Panel Flutter Considering the Effect of Convective Active Cooling

The aeroelastic characteristics of the panel under the action of coolant are obviously different from the flutter characteristics of the traditional panel. In order to solve this problem, the dynamics model of the panel flutter was established in this paper based on von Karman’s large deformation theory and the Kirchhoff–Love hypothesis. The panel dynamics equations were discretized into constant differential equations with finite degrees of freedom by Galerkin’s method, and solved by the fourth Runge–Kutta method in the time domain. The nonlinear modified piston theory was used to predict the unsteady aerodynamic loads, and the accuracy of the flutter analysis model was verified. On this basis, the effects of the head-panel pressure of coolant, the pressure drop ratio, the coolant injection direction, and the inertial resistance and viscous resistance on panel stability and flight stability were investigated, respectively. The results showed that reducing the pressure drop ratio, and reducing or increasing the head-panel pressure (valuing away from the freestream pressure) can improve the critical dynamic pressure when bifurcation occurs. At M∞=5.0, the pressure drop ratio causes a 22.1% increment in the critical dynamic pressure. The influence of the coolant injection direction on the panel bifurcation is mainly influenced by the head-panel pressure. The inertial resistance slows down the convergence process of the panel response, increases the limit cycle amplitude, and reduces the critical dynamic pressure of the panel, while the viscous resistance plays the opposite role. Based on these conclusions, this paper finally proposes the suppression method of panel fluttering from head-panel pressure, inertial resistance, viscous resistance, etc.

Modeling nonlinear flutter behavior of long‐span bridges using knowledge‐enhanced long short‐term memory network

AbstractThe nonlinear characteristics of bridge aerodynamics preclude a closed‐form solution of limit‐cycle oscillation (LCO) amplitude and frequency in the post‐flutter stage. To address this issue, a long short‐term memory (LSTM) network is utilized as the reduced‐order modeling of nonlinear aeroelastic forces on the bridge deck section, and it is repeatedly employed to generate force inputs at spanwise nodes of a three‐dimensional (3D) finite element model (FEM) of the long‐span bridge (using spatial beam elements). All LSTM networks are dynamically coupled through FEM, and the 3D nonlinear flutter response is accordingly obtained. To improve the simulation accuracy and reduce the required training data of the standard LSTM network, both general knowledge (motivated by the gating mechanism and mathematical models for information processing) and domain knowledge (resulting from the basic understanding of bridge aerodynamics) are leveraged to, respectively, customize the LSTM cell and network architecture. In addition, a fast‐training algorithm effectively combining the linear convergence of stochastic gradient descent and superlinear convergence of modified Broyden–Fletcher–Goldfarb–Shanno is developed to improve the training efficiency of the obtained knowledge‐enhanced LSTM network. To further advance the computational efficiency of the coupled LSTM‐FEM nonlinear flutter analysis, the convolution‐based numerical integration is adopted in the finite element modeling of long‐span bridge dynamics. A case study of a long‐span suspension bridge under strong winds demonstrates the proposed 3D nonlinear flutter analysis presents high simulation efficiency and accuracy and can be utilized to effectively obtain the nonlinear LCO characteristics in a wide range of post‐flutter wind speeds.

High-Fidelity Aerostructural Optimization with a Geometrically Nonlinear Flutter Constraint

When designing aircraft, avoiding dynamic aeroelastic instabilities such as flutter is a key requirement. One way to meet this requirement is to use a multidisciplinary design optimization subject to a flutter constraint. Flutter-constrained design optimizations have used geometrically linear detailed models, which do not accurately predict flutter for very flexible aircraft, or geometrically nonlinear low-order models, which do not accurately trade off cruise range and structural mass. This paper presents a framework for integrating a geometrically nonlinear, subsonic flutter constraint that captures the large in-flight deflections of very flexible aircraft into high-fidelity gradient-based aerostructural optimization. The cruise range and stress constraints are computed accurately with detailed aerostructural analyses, which use a built-up finite element model coupled to Reynolds-averaged Navier–Stokes computational fluid dynamics. The detailed model is condensed to a low-order aeroelastic model to compute the geometrically nonlinear flutter constraint and its adjoint derivatives with computational cost and robustness suitable for optimization. The framework is demonstrated by maximizing the cruise range of a subsonic high-aspect-ratio wing with respect to panel thicknesses, sweep, and span. The impact of the geometrically nonlinear flutter constraint highly depends on the in-flight deformation level. At low deflection levels, sweeping the wing backward is the most effective flutter prevention method, and the flutter constraint has little impact on the achievable cruise range. At high deflection levels, shortening the wing span is necessary to suppress flutter, reducing the achievable cruise range by up to 5.9%. This work is a step toward making multidisciplinary design optimization a practical tool for designing the energy-efficient, very flexible aircraft of the future, which require geometrically nonlinear flutter analyses early in the design cycle to prevent flutter.

Numerical Stabilization for Flutter Analysis Procedure

Severe mode switching is often observed when the PK-method is used in the flutter analysis of complex aircraft configurations, in particular when nearly 100 vibrational modes are considered. In the commonly used commercial software NASTRAN, the resulting eigenroots are sorted in an ascending order of frequency. Therefore, the appearance of massive mode-switching instances cannot be avoided in the PK-method flutter analyses, especially for engineering applications with real-world complex configurations. In this study, as a post-processing procedure, an extensive sorting capability was developed in order to compensate for NASTRAN’s lack of a mode-tracking procedure in between the airspeed steps. The capability was developed based on both the complex eigenvalues and their corresponding eigenvectors. In addition, numerical techniques commonly used in computational fluid dynamics (CFD) were introduced to improve the convergence of the traditional PK-method. A hybrid approach was applied to the initial guess of the reduced frequency, followed by a deferred correction scheme for the PK-iteration process. Additionally, mode matching was specifically addressed when locking eigenroots onto the aerodynamics within the PK iterations. In addition to the PK iterations, a damping iteration or modified g-method was implemented by extending the PK-method solver. The combination of these special techniques effectively improved the numerical stability of the iterations in the stability eigensolution process and significantly reduced the appearance of the misleading mode switching, minimizing risks in aircraft flight.

Flutter analysis including structural uncertainties using a relaxed LMI-based approach

Flutter analysis including structural uncertainties using a relaxed LMI-based approach

Stability and dynamical analysis of whirl flutter in a gimballed rotor-nacelle system with a smooth nonlinearity

AbstractWhirl flutter is an aeroelastic instability that affects aircraft with propellers/rotors. With their long and flexible rotor blades, tiltrotor aircraft are particularly susceptible. Whirl flutter is known to have destroyed aircraft and in the best case it constitutes a fatigue hazard. The complexity of whirl flutter analysis increases significantly with the addition of nonlinearities, due to the more complex dynamical behaviours that emerge as a result. Most whirl flutter stability analyses in current literature are grounded in linear theory, preventing the full discovery of the nonlinearities’ effects. Continuation and bifurcation methods (CBM) may instead be used to fully appreciate and analyse the effects of the presence of nonlinearities. Previous CBM-based work on nonlinear gimballed hub rotor-nacelle models, representing those found on tiltrotor aircraft, are capable of whirl flutter in parametric regions declared safe by linear analysis. Furthermore, it was found that they are capable of complex behaviours including limit cycle oscillations, quasi-periodic behaviour and even chaos, though the whirl flutter implications of such behaviours has not been explored. This paper investigates the impact of a smooth structural nonlinearity on the whirl flutter stability of a basic gimballed rotor-nacelle model, compared to its baseline linear stiffness version. A 9-DoF model with quasi-steady aerodynamics, a flexible wing and blades that can move both cyclically and collectively in both flapping and lead-lag motions, producing gimbal flap-like behaviour, was adopted from existing literature. A smooth stiffness nonlinearity was introduced in the blade flapping stiffness and CBM was used to find the new whirl flutter behaviours created by the presence of the nonlinearity. Time simulations, Poincaré sections and spectral analysis were then used to investigate the various behaviours found. This in turn allowed recommendations to be made concerning preferable and/or hazardous parameter combinations of use to the tiltrotor designer.

Nonlinear Flutter Analysis of Labyrinth Seals

Abstract A simple nonlinear model to describe labyrinth seal flutter has been developed to assess the aeromechanic stability of straight-through labyrinth seals subjected to large gap variations. The model solves the one-dimensional integral mass, momentum, and energy equations of the seal for a prescribed motion numerically until a periodic state is reached. The model accounts for the effect, previously neglected, of high clearance variations on the stability. The results show that when the vibration amplitudes are small, the work-per-cycle coincides with the prediction of the Corral and Vega model (2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background,” ASME J. Turbomach., 140(10), p. 121006) and Corral et al. (2021, “Higher-Order Conceptual Model for Seal Flutter,” ASME J. Turbomach., 143(7), p. 071006), but for large vibration amplitudes nonlinearities alter the stability limit. In realistic cases, when the discharge time of the seal is much longer than the vibration period, the nonlinear effects are significant and tend to increase the unstable range of operating conditions. Furthermore, seals supported either on the high-pressure or low-pressure sides, stable for small vibration amplitudes, can destabilize when the vibration amplitude increases. The linear stability, though close in many situations to the nonlinear threshold, is not conservative, and attention must be paid to nonlinear effects.

Flutter analysis and wind-tunnel experiments of a flat plate suspended by wires

Flutter analysis and wind-tunnel experiments of a flat plate suspended by wires

Flutter analysis of mistuned bladed disk

Flutter analysis of mistuned bladed disk

Geometrically Nonlinear Flutter Analysis Based on CFD/CSD Methods and Wind Tunnel Experimental Verification

This study presents a high-speed geometrically nonlinear flutter analysis calculation method based on the high-precision computational fluid dynamics/computational structural dynamics methods. In the proposed method, the aerodynamic simulation was conducted based on computational fluid dynamics, and the structural model was established using the nonlinear finite element model and tangential stiffness matrix. First, the equilibrium position was obtained using the nonlinear static aeroelastic iteration. Second, the structural modal under a steady aerodynamic load was extracted. Finally, the generalized displacement time curve was obtained by coupling the unsteady aerodynamics and linearized structure motion equations. Moreover, if the flutter is not at a critical state, the incoming flow dynamic pressure needs to be changed, and the above steps must be repeated until the vibration amplitude are equal. Furthermore, the high-speed geometrically nonlinear flutter of the wing-body assembly model with a high-aspect ratio was investigated, and the correctness of the method was verified using high-speed wind tunnel experiments. The results showed that the geometric nonlinearity of the large deformation of the wing caused in-plane bending to become a key factor in flutter characteristics and significantly decreased the dynamic pressure and frequency of the nonlinear flutter compared to those of the linear flutter.

Influences of Attack Angles on Aerodynamic Derivatives and Flutter Characteristics of Flat Box Girders

The flutter response of Nanjing Fourth Bridge flat box girder under different wind attack angles was tested in detail through sectional model test. The evolution of unsteady and steady critical amplitude with wind speed was discussed. Based on the amplitude envelope of the flutter response and the Hilbert transform, the amplitude- dependent modal damping of the system is identified, and the mechanism of the flutter mode change in the wind angle of attack is initially explained. Secondly, the modal parameters of the system under different wind attack angles were extracted. Based on the bimodal coupled flutter analysis method, the nonlinear flutter derivatives of the section under different wind attack angles were identified, and the change law of the amplitude dependence of the key flutter derivatives on the wind attack angle and the potential influence on the flutter morphology and characteristics of the section were studied. Finally, the effect of wind attack angle on uncoupled and coupled aerodynamic damping is analyzed by deconstructing the modal damping one by one, and the dynamic mechanism of the differential flutter performance caused by fractional damping is illustrated.

Aeroelastic Tailoring of Variable Stiffness Composite Laminated Quadrilateral and Circular Plates in Supersonic Flow Using Isogeometric Approach

In this study, a cubic NURBS-based isogeometric finite element method is developed to study the aeroelastic tailoring of variable stiffness composite laminated (VSCL) plates, including skew, skew-tapered, tapered, and circular shapes based on third-order shear deformation theory. Also, the first-order piston theory is employed to approximate aerodynamic loads with arbitrary yaw flow angles over the plate area to establish aeroelastic equations. The NURBS basis functions are then utilized to simulate exact geometries and estimate variable fields for discretizing governing equations by well-known isogeometric analysis. Finally, the free vibration and flutter analysis of a VSCL quadrilateral and circular plate will be presented via the obtained eigenvalue problem. The achieved results are compared with the available results in the literature to prove the accuracy and validity of the present method. The effect of different parameters such as the flow yaw angle, end and middle-length fiber orientation, longitudinal to transverse Young’s modulus ratio, geometric shape, boundary conditions, and turning symmetric layup to asymmetric layup is carried out on the critical flutter aerodynamic pressure and natural frequencies.