Critical Flutter Speed Research Articles

Investigation of Additional Mass Effect on Dynamic Wing Model Stability in Airflow

The paper investigates a dynamic stability of the wing model in the flow of incoming air. As is known, at a certain flow rate, called critical, there occurs a phenomenon of self-excited non-damping flexural-and-torsional self-vibrations, called flutters. The paper considers an anti-flutter approach that is the placement of additional weight on the elastic elements (springs) in the wing model. Thus, a three-stage wing model is under consideration while the publications concerning this problem more often describe a two-stage wing model. The paper is a natural sequel to the authors’ first paper [9] where a two-stage wing model was considered in detail. It continues and develops research in this area, conducted by many famous scientists, such as V.L. Biderman, S.P. Strelkov, Ya.G. Panovko, I.I. Gubanova, E.P. Grossman, J.C. Fyn and many others who have investigated this phenomenon. It is also necessary to mention the scientists, namely Keldysh M.V., Reese P.M., Parkhomovsky Y. M., etc. who not only studied this phenomenon, but developed anti-flutter methods for it.It should be noted that not only scientists-theoreticians, but also test pilots, in particular M.L. Gallay [8], contributed to the solution of the flutter problem. The paper describes in detail a derivation of the linear differential equations of small vibrations of a wing model with additional weight in the flow, determines the eigenfrequencies and forms of flexural-and-torsional vibrations, checks their orthogonality, explores the forced vibrations under aerodynamic force and moment, and estimates a critical flow rate for a number of system parameters, namely a mass of the additional weight and the rigidity of its suspension. The conclusion is drawn that these parameters effect on the critical rate. Based on the calculation results, one can come to the conclusion on the additional weight effect on the critical flutter speed and on how relevant the anti-flutter method is. The given paper may be of interest both for students of technical specialties who learn the theory of mechanical vibrations, and for engineers majoring in aero-elasticity and dynamic stability of the elements of mechanical systems.

Comparison of low, medium and high fidelity numerical methods for unsteady aerodynamics and nonlinear aeroelasticity

The unsteady aerodynamic and aeroelastic behavior of a 2D wing section with and without flap is analyzed with Theodorsen theory and Unsteady Vortex Lattice Method (low fidelity), Euler (medium fidelity) and Reynolds-Averaged Navier Stokes (high fidelity) methods. The aeroelastic studies are carried out for linear cases and non-linear structural configurations presenting cubic stiffness and freeplay. The critical flutter speeds as well as the limit cycle oscillations present in the non-linear cases are compared. The methods show good agreement for the cases studied.

Structural integrity assessment on cracked composites interaction with aeroelastic constraint by means of XFEM

In this paper, a novel approach in assessing the structural integrity of cracked composite plates under the aeroelastic condition by using XFEM is presented. To the authors’ knowledge, this is the first time that aeroelastic condition is coupled in XFEM to model the crack propagations. Previous researches from the literature had only considered a static crack condition. This research focuses on determining the first failure experienced by the cracked composite plate, either the crack will propagate causing a fracture, or the composite plate will fail due to aeroelastic instability imposed at the critical flutter speed. The proposed scheme is used to solve the limitation in XFEM within Abaqus that only general static and implicit dynamic analysis can be performed. The structure is assumed to interact with minimal gust, and the deflections by time are expressed in the equation of periodic motion based on Fourier Series Function (FSF). The results show that at a particular fibre orientation, once the damaged composite plate is deformed due to the dynamics load at dive speed, it fails due to the crack propagation first instead of the flutter. In contrast, another fibre configuration shows good resistance to crack propagation and fails due to flutter instability.

Thermoelastic stability of closed cylindrical shell in supersonic gas flow

In this paper the problem of linear stability of a closed cylindrical shell under the action of both non-uniform temperature field and supersonic gas flow is considered. The stability conditions for the unperturbed state of the aerothermoelastic system are obtained. It is shown that, by the combined action of the temperature field and the ambient supersonic flow, the process of linear stability can be controlled and the temperature field affects significantly the critical flutter speed.

Improving Aileron Effectiveness Based on Changing the Position of Aileron Connectors

In this paper, the design concept of the aileron with a fixed connector and a moving connector has been explored due to the improvement of aileron effectiveness. As usual, aileron reversal or the blocking phenomenon of multijoint fixed ailerons is a hard nut to crack. In the present research, in order to improve aileron effectiveness, several examples are studied. The connection position influences the stress, displacement, load distribution, and control effectiveness of the aileron or critical flutter speed. As the joint positions are different, the wing-aileron connection stiffness is also changing. The sample of the beam shows the weight reduction. The plate simulation indicates the decreased deformation and the better load distribution. The aileron trimming demonstrates the improvement of aileron effectiveness. And the flutter speed coupled with the aileron is different. All of these examples indicate the feasibility of this new concept of the aileron design, which means improving aileron effectiveness based on changing the position of aileron connectors. Finally, three different modes for wing-aileron connections are suggested for reference.

The effects of structural and aerodynamic nonlinearities on the energy harvesting from airfoil stall-induced oscillations

An airfoil may undergo stall-induced oscillations beyond the critical flutter speed with amplitudes determined by aerodynamic nonlinearities due to the dynamic stall. Stall-induced oscillations yield intense periodical motions that can be used to convert the airflow energy into electrical power. The inclusion of structural nonlinearities contributes to the complexity of the aeroelastic response. In this sense, the present work models and analyzes for the first time the effects of structural and aerodynamic nonlinearities in the potential of extracting energy from pitching and plunging motions of an airfoil during stall-induced oscillations. A computational model is employed, based on the electro-aeroelastic differential equations modeling a typical aeroelastic section with two degrees of freedom with an electrical generator connected to the pitching motion and a piezoelectric element connected to the plunging motion. The Beddoes–Leishman semi-empirical model is used to represent the unsteady aerodynamic loading. Concentrated structural nonlinearities, such as the hardening effect and free-play, are also considered. Bifurcation diagrams and harvested power calculations are used to analyze the performance of each energy harvesting scheme. The results show that nonlinear pitching stiffness reduces the average harvested power from this degree of freedom in a range of wind speeds. However, the presence of a free-play spring reduces the flutter velocity and initiates the harvesting at lower wind speeds. In conclusion, the present electro-aeroelastic model can be used to find optimal parameters of a harvester from airfoil stall-induced oscillations for a specific application.

Influence of stochastic perturbations of composite laminate layups on the aeroelastic flutter of a cantilevered plate wing

A numerical study of the effect of uncertainties in ply angles and thicknesses on the flutter speed of a cantilevered composite plate wing was conducted in this paper. Reduction of the number of uncertain parameters was possible thanks to the use of the polar method, which also enabled a systematic analysis of the influence of material symmetries. From the polar domain of orthotropic laminates, several stacking sequences were reconstructed in order to propagate parametric uncertainties. Typical fabrication uncertainties on ply thicknesses and angles were considered in order to quantify their influence on the probabilistic aeroelastic response. The reduction of the set of stochastic parameters by the polar method enabled the use of a polynomial-chaos approach which was combined with machine-learning techniques in order to deal with the correlation and with discontinuities in the response surface. Results reveal that possible manufacturing tolerances cause significant deviations in the critical flutter speed from the nominal value, especially when mode switches occur. As these deviations surpass classical dimensioning margins, uncertainty quantification approaches can provide added safety.

An efficient method for flutter stability analysis of aeroelastic systems considering uncertainties in aerodynamic and structural parameters

Abstract The aim of this work is to propose a novel numerical method for analyzing the flutter stability of aeroelastic systems considering uncertain parameters. Unlike the probabilistic method which is dependent on large quantities of statistical information, interval models are utilized to quantify the uncertain aerodynamic and structural parameters. An interval-form of the aeroelastic equation is established by substituting interval variables into a deterministic aeroelastic model. The flutter stability of an aeroelastic system is analyzed as a generalized interval eigenvalue problem via eigenvalue-based approach. By using the sensitivity analysis based vertex method (SAVM), interval bounds on eigenvalues can be calculated through solving two additional deterministic eigenvalue problems. A novel uncertain propagation method, called Bernstein polynomial method (BPM), is proposed to calculate the interval bounds on eigenvalues. The range of critical flutter speed can be predicted based on the upper and lower bounds on the maximum real part of all eigenvalues. For comparison, the perturbation-based probabilistic uncertainty propagation method (PPUPM) is given to determine the bounds on eigenvalues and the critical flutter speed. Numerical results demonstrate that BPM is consistent with Monte-Carlo simulation method within significantly less computation time and verify the compatibility between BPM and PPUPM.

Nonlinear supersonic flutter for the viscoelastic orthotropic cylindrical shells in supersonic flow

On the example of an orthotropic shell, the problems of the dynamics of thin-walled structures under aerodynamic loading are studied, taking into account the viscoelastic properties of material and geometric nonlinearity. The aerodynamic pressure is determined using the AA. Ilyushin's piston theory. Equations of motion relative to displacements are described by a system of integro-differential equations in partial derivatives. Using the Bubnov–Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to a system of ordinary integro-differential equations, where time is an independent variable. Solutions of integro-differential equations are determined by a numerical method based on the elimination of the singularity in the relaxation kernel of the integral operator. Computational algorithms and applied programs have been developed to solve the problems on the nonlinear flutter for viscoelastic elements of an aircraft. The critical flutter speed for the viscoelastic orthotropic cylindrical shells is determined. It is established that an account of viscoelastic properties of shell material leads to a decrease in the critical flutter.

Flutter of a Laminated Cantilever Cylindrical Shell with a Ring-Stiffened Edge

The aeroelastic stability of a medium length cantilever cylindrical shell stiffened by an edge ring with the outer surface exposed to supersonic gas flow is investigated. The shell motion is described by the equations of the semi-membrane theory for laminated shells and considered with various end conditions. The dependences of the critical flutter speed on the dimensions of the ring cross-section, the value of the structural damping coefficient, the flow parameters, and the type of boundary conditions are obtained.

Aeroelastic Instability of Cantilever Wing with Added Engine Mass and Thrust Loads Under the Gust Envelope

Dynamic analysis and instability prediction of immersed bodies under variable loading conditions is an important issue in fluid dynamics. This work presents the dynamic analysis of a wing section by considering the engine mass and the resulting thrust effect using a distributed parameter model. The equations of motion of cantilever wing are obtained using the extended Hamilton’s principle by accommodating the engine mass and the follower force terms. Initially, the stability regions of the clean wing without engine are identified using modal reduction scheme. The critical frequencies and flutter speed obtained from the model are validated with available results. In order to study the influence of other parameters such as position of engine mass, number of store masses and the generated thrust, a series of parametric studies are conducted. To make the study more realistic, the cantilever wing with engine mass is further subjected to a vertical discrete gust loading. It is found that the model is reliable and interactive in further analysis.

A parametric study of flutter behavior of a composite wind turbine blade with bend-twist coupling

Now a days wind turbine blades are generally designed to have length as high as 60 m or more to maximize power production. Aeroelastic instabilities such as flutter are major concerns for these long, flexible and slender blades. Stiffness coupling between bending and twisting modes can be used to improve the aeroelastic performance of such blades. In composite blades bend twist coupling can be achieved by imparting unbalance in the lamination sequence. In the present work, a parametric study has been conducted to study the effect of unbalances in different parts of a wind turbine blade on flutter instability. An eigenvalue-based approach has been used for flutter analysis. It has been observed that flap-torsional stiffness has high impact on critical flutter speed. The critical flutter speed is increased by 40% with flap-torsional stiffness due to the unbalance in the entire section of the blade with symmetric skin, while for asymmetric skin; the achievable increment is 100%. The unbalance in the spar cap of the blade has less critical flutter speed as compared to the unbalance in the entire section of the blade. Unbalance in the entire section of the blade with asymmetric skin can lead to highest flutter speed.

Predicting the flutter speed of a pedestrian suspension bridge through examination of laboratory experimental errors

The paper investigates experimental error propagation and its effects on critical flutter speeds of pedestrian suspension bridges using three different experimental data sets: pressure coefficients, aerodynamic static forces and flutter derivatives. The three data sets are obtained from section model measurements in three distinct laboratories. Data sets are used to study three different geometries of pedestrian suspension bridges. Critical flutter speed is estimated using finite-element nonlinear analysis, numerical 2-DOF generalized deck model and 3-DOF full-bridge model. Flutter probability, contaminated by various experimental error sources, is examined. Experimental data sets are synthetically expanded to obtain two population sets of deck wind loads with 30 and 5 · 105 realizations, respectively. The first set is obtained using Monte-Carlo simulation approach, whereas the second one is determined using Polynomial chaos expansion theory and a basis of Hermite polynomials. The numerically-determined probability density functions are compared against empirical probability histograms (pdfs) by Kolmogorov-Smirnov tests.

Vibration analysis of a thin eccentric rotating circular cylindrical shell

In this study, the vibration characteristics of a thin eccentric rotating circular cylindrical shell with simply supported boundary conditions are studied. Energy formulations based on Flügge’s thin shell theory, Hamilton’s principle, and the method of linear approximation are applied to derive the governing equations of motion. In addition to the effects of centrifugal and Coriolis forces, the effect of nonuniform initial stresses resulting from eccentric rotation are taken into account. The natural frequencies of the shell with respect to rotating speed and eccentricity are obtained using Galerkin’s method. To validate the present analysis, comparisons are carried out with the results in published literatures and finite element analysis, and good agreements are obtained. The effect of the eccentricity on the natural frequency of the eccentric rotating cylindrical shell is investigated. Some further numerical results are given to illustrate the irregular frequency mutation behaviors resulting from the eccentricity. The effects of the eccentricity on the critical speed and flutter speed of the eccentric rotating circular cylindrical shell are also investigated.

Full Aeroelastic Model Testing for Examining Wind-Induced Vibration of a 5,000 m Spanned Suspension Bridge

This paper presents an experimental investigation on wind-induced vibrations of a suspension bridge with ultimate main span length, including flutter and buffeting. Since the upper limit of a suspension bridge’s main span can reach more than 5,000m based on strength and weight of steel main cables, a feasible prototype with a span arrangement of 2,000m+5,000m +2,000m has been proposed. In order to improve flutter stability, a twin box girder has been designed with a 40m slot in center and two 20m wide decks suspended by four main cables. Its full aeroelastic model was designed and manufactured with the geometrical scale of 1:620, and the wind tunnel testing was carried out under smooth flows and turbulent flows for different angles of attack. A big difference in critical flutter speed was found between the proposed slotted girder and corresponding slot-sealed girder, which verifies the necessity of a widely-slotted twin box girder for a super-long suspension bridge. Among three angles of attack, the critical flutter speed under smooth flow has the maximum value of 80.9 m/s at -3° and the minimum value of 51.4m/s at 3°. On-coming turbulence will not only cause buffeting responses but also influence the critical flutter speed in an unfavorable way.

Examination of experimental errors in Scanlan derivatives of a closed-box bridge deck

The objective of the investigation is the analysis of wind-tunnel experimental errors, associated with the measurement of aeroelastic coefficients of bridge decks (Scanlan flutter derivatives). A two-degree-of-freedom experimental apparatus is used for the measurement of flutter derivatives. A section model of a closed-box bridge deck is considered in this investigation. Identification is based on free-vibration aeroelastic tests and the Iterative Least Squares method. Experimental error investigation is carried out by repeating the measurements and acquisitions thirty times for each wind tunnel speed and configuration of the model. This operational procedure is proposed for analyzing the experimental variability of flutter derivatives. Several statistical quantities are examined; these quantities include the standard deviation and the empirical probability density function of the flutter derivatives at each wind speed. Moreover, the critical flutter speed of the setup is evaluated according to standard flutter theory by accounting for experimental variability. Since the probability distribution of flutter derivatives and critical flutter speed does not seem to obey a standard theoretical model, polynomial chaos expansion is proposed and used to represent the experimental variability.

Multiobjective optimization of an aircraft wing design with respect to structural and aeroelastic characteristics using neural network metamodel

The multidisciplinary design optimization (MDO) is an important concept that focuses on bringing together disciplines involved with machine design. It is possible to use MDO in any stage of an aircraft design, that is in the conceptual, preliminary, or detailed design, as long as the numerical models are fitted to each of these stages. This work describes the development of a multidisciplinary design optimization applied to flexible aircraft wings, with respect to structural and aeroelastic characteristics. As tools for the aircraft designer, the numerical models must be fairly accurate and fast. Therefore, metamodels for the critical flutter speed prediction of aircraft wings were considered, thereby reducing significantly the computational cost of the optimization. For this purpose, artificial neural networks (NN) metamodeling is evaluated, based on their inherent properties in dealing with complex mappings. The NN metamodel is prepared using an aeroelastic code based on finite-element model coupled with linear potential aerodynamics. Results of the metamodel performance are presented, from where one can note that the NN is well suited for flutter prediction. Multiobjective optimization (MOO) using the genetic algorithm (GA) based on non-dominance approach is considered. The objectives were the maximization of critical flutter speed and minimization of structural mass. One case study is presented to evaluate the performance of the MOO, revealing that overall optimization process actually achieves the search for the Pareto frontier.

Experimental Evaluation of the Critical Flutter Speed on Wings of Different Aspect Ratio

Experimental Evaluation of the Critical Flutter Speed on Wings of Different Aspect Ratio

Dynamics and vibration analysis of suspended microchannel resonators based on strain gradient theory

In this paper, dynamics of a suspended microchannel resonator (SMR) will be derived using the strain gradient theory. Accordingly, the size dependent governing equation and corresponding boundary conditions will be obtained using the extended Hamilton’s principle for open systems. The proposed strain gradient theory has three length scale parameters which can be reduced to the modified couple stress theory and the classical theory when two of three length scale parameters or all of them are set to zero, respectively. Also, the size effect of micro-flow associated with the flow velocity profile will be considered in the governing equation of motion. The stability analysis is then carried out to obtain complex frequencies and critical flutter speeds. Finally, the effects of flowing particle in the microchannel and the associated frequency shifts induced by the added mass will be studied.

Flutter performance and aerodynamic mechanism of plate with central stabilizer at large angles of attack

To analyze the effects of a central stabilizer on the flutter performance at large angles of attack, this study takes the ideal plate as a section of a bridge deck. The aerodynamic characteristics of stationary cross sections are examined using computational fluid dynamics simulations, and the flutter derivatives are extracted by forced vibration. The critical flutter speed of a target bridge is then calculated, and the aerodynamic mechanism of the central stabilizer is discussed from the work done by aerodynamic forces’ perspective. The results show that use of a central stabilizer with lower heights favors flutter stability at smaller angles of attack by improving the participation level of heaving motion, but the stability of the systematic heaving motion will decrease if the stabilizer is too high, leading to galloping. At larger angles of attack, where the movement of a big vortex causes the occurrence of torsional flutter, the stabilizer can hinder the movement of the vortex if they are on the same side, and the critical flutter speed increases with the increase in stabilizer height.