Aeroelastic analysis and flutter control of wings and panels: A review

Zhang Y., Li Z., Xu K., Zang J.

Herein, a novel pyramid lattice sandwich structure with the active variable stiffness (AVS) is proposed, which consists of a proportion integration (PI) active controller, a piezoelectric actuator, and a variable stiffness device. The principle of AVS is to process the real-time vibration feedback signal of the lattice sandwich beam by using the PI controller and the piezoelectric actuator to change structural stiffness continuously. The structure has excellent self-adjusting and active vibration reduction effect. Based on the supersonic piston theory, Hamilton's principle, and the assumed modes method, the dynamics equations of the whole structure are established. The vibration reduction and energy dissipation of lattice sandwich beams with AVS and without AVS are analyzed by using the Runge-Kutta algorithm. Moreover, the relevant parameters of PI controller, positive stiffness, negative stiffness, incoming flow velocity, damping coefficient, and installation position are compared and analyzed, respectively. The results indicate that the novel lattice sandwich structure with AVS can achieve ideal vibration reduction effect, and the efficiency can be improved by adjusting the parameters appropriately.

Chai Y., Du S., Li F., Zhang C.

In this paper, an effective theoretical method is developed and experimentally validated for investigating the vibration behaviors of the simply supported sandwich plates with a pyramidal truss core on elastic foundation. An adjustable sliding support frame that can adapt to variations in the plate length and width is designed to realize the simply supported boundary conditions. The kinematic relations of the sandwich plates are derived, and the constitutive or stress–strain relationships for the face sheets and pyramidal truss core are established. The governing equations of motion are derived by Hamilton’s principle, and the structural vibration characteristics are conveniently analyzed. The structural natural frequencies calculated from the present theoretical method are compared with the experimental and FEM simulation results, which validates the correctness and accuracy of the present theoretical model. The effects of the geometric parameters, material properties and combinations as well as elastic foundation on the vibration behaviors are analyzed in details. The key contributions of this paper are the establishment of the dynamic model, the design of the adjustable sliding support frame simulating the simply supported boundary conditions and the systematic parametrical analysis of the structural vibration behaviors by the theoretical and experimental methods. • A theoretical method is developed for studying vibration behaviors of pyramidal lattice sandwich plates on elastic foundation. • A sliding support frame is designed to realize the simply supported boundary conditions. • An experimental method is proposed to analyze the vibration characteristics of sandwich plates. • The effects of the structural parameters on the natural frequencies are investigated systematically.

Khaniki H.B., Ghayesh M.H., Hussain S., Amabili M.

This study investigates the effects of geometric nonlinearities on the dynamical behaviour of carbon nanotube (CNT) strengthened imperfect composite beams by considering both axial and transverse motions. For the given general model of the beam, the system modelling has been adopted from the literature and the nonlinear dynamic response in presence of an external harmonic load is examined for the first time in the case of axially functionally graded (AFG) CNT fibre, which is used for strengthening the structure. Porosity imperfection with the ability to vary though the thickness is modelled using simple, closed and open-cell models; the porosity variation is formulated using uniform, linear, symmetric and un-symmetric models. The geometrical imperfection is considered by allowing the beam to have an initial curved longitudinal axis and the mass imperfection is modelled by introducing a concentrated mass at a certain point of the beam. Using a combination of the Galerkin scheme together with dynamic equilibrium technique, the influence of different imperfections and porosities on the frequency response of the system is examined. It is shown that, for the case of AFG CNT strengthened beam, geometrical imperfection can change the nonlinear response from a hardening to a softening behaviour. Besides, the importance of considering the interaction between axial and transverse motion is examined in detail. The influence of lumped mass imperfection and its position is also studied showing that this type of imperfection can change the nonlinear behaviour of the system significantly. Moreover, the influence of increasing the CNT volume fraction and functionally spreading the CNTs through the length is discussed. The results are useful for analysing the resonance phenomena in strengthened structures facing various imperfections.

Guo Z., Hu G., Sorokin V., Tang L., Yang X., Zhang J.

Though lightweight sandwich structures have been extensively applied in practical engineering, it remains a challenge to control wave propagation and vibration in these structures in a low-frequency range. In this work, the band structure of flexural waves in a metamaterial sandwich beam (MSB) with hourglass lattice truss core is investigated using the transfer matrix method (TMM). The hourglass truss structure with lumped masses is modelled as a series of local resonators with determined equivalent stiffnesses and masses. A metamaterial dual-beam (MDB) model is then established to describe the MSB, and the MDB model is noted to be equivalent to the conventional metamaterial beam (CMB) model under base excitation. The MSB is further studied directly by the finite element method that confirmed the MSB can be represented by the CMB through the transmittance analysis and band structure analysis. Subsequently, parametric study is performed to investigate the effects of the material and structural parameters on the band structures of the MSB. This work provides a roadmap of modelling of lightweight lattice sandwich beams with complex core structures and presents guidelines for applying sandwich beams to control wave propagation.

AminYazdi A.

In this paper, flutter of geometrical imperfect functionally graded carbon nanotubes (FG-CNTs) doubly curved shell subjected to a supersonic flow is investigated. For this purpose, the imperfect doubly curved shell is reinforced by four different carbon nanotubes (CNTs) distributions in the thickness direction. The Hill’s elastic moduli are used to obtain the effective material properties of FG-CNTs doubly curved shell. The piston aerodynamic theory and von Karman geometrical nonlinearity terms are used to study large deflection flutter analysis of FG-CNTs imperfect shell. The effect of different parameters including large deflection, geometrical imperfection and CNTs volume fraction on critical flutter pressure of doubly curved shells are studied. According to the results, distributions with poor CNTs in the middle of thickness are more efficient in improving critical flutter pressure. Additionally, the effect of shell imperfection on flutter pressure is more considerable than CNTs volume fraction and distributions. • Aeroelastic stability of functionally graded carbon nanotubes composite shell is presented. • The effect of geometrical imperfection is considered. • The Hill’s elastic coefficients are used to obtain effective material properties. • He’s homotopy perturbation method is utilized to predict critical flutter pressure. • The effect of large deflection is considered.

Xu J., Gao Q., Lv H., Yang Y., Fu B.

AbstractThe control of aeroelastic response of a wing section with influence of the fuel sloshing in external tank is examined through analytical studies. Based on the simplified mass-spring-damper...

Freydin M., Dowell E.H.

A recent structural model of a plate is extended to include a nonuniform temperature differential that varies in time using a modal expansion. The nonlinear structural plate model with first-order ...

Camacho P., Akhavan H., Ribeiro P.

• Modelling of a hybrid multiscale composite with CNTs and curvilinear fibres. • Using a new approach to obtain shear elastic moduli of composites with fibres. • Application of a new sinusoidal fibre path. • Aeroelastic analysis of hybrid composite laminates . • Effects of CNT content and fibre orientation on aeroelastic instabilities. In this paper, cantilever laminated composite plates, subjected to supersonic airflow, are studied in the linear elastic regime. The considered material is a multiscale three-phase composite, constituted by epoxy resin reinforced with multi-walled carbon nanotubes and curvilinear carbon fibres. The orientation of the fibres is defined using three different functions. A model based on a third-order shear deformation theory and a p -version finite element is applied. Furthermore, a hierarchical approach is applied to characterise the mechanical properties of the composite material. A combination of adequate micromechanics based models, including a modified version of the Halpin-Tsai model, the Rule of Mixtures, a unit cell-based model, and the Chamis model, is implemented. The aeroelastic analysis is performed considering the linear piston theory to evaluate flutter (dynamic instability) and divergence (static instability) in such structures. The improvements achieved through the combination of carbon nanotubes and curvilinear fibres on the instabilities are explored.

Qiao S., Jiao J., Ni Y., Chen H., Liu X.

High aspect ratio wing (HARW) structures will deform greatly under aerodynamic loads, and changes in the stiffness will have a great impact on the flutter characteristics of such wings. Based on this, this paper presents an effective method to determine the effect of the stiffness on the flutter characteristics of HARWs. Based on the calculation theory of the mechanical profile of thin-walled structures, the torsional stiffness and bending stiffness of the wing are obtained through calculation. We use the fluid-structure coupling method to analyze the flutter characteristics of the wing, and we use our research results based on the corotational (CR) method to perform structural calculations. The load is calculated using a computational fluid dynamics (CFD) solver. The results show that, compared with the original wing, when the bending stiffness and torsional stiffness of the wing along the spanwise direction increase by 8.28% and 5.22%, respectively, the amplitude of the flutter decreases by approximately 30%. Increasing the stiffness in the range of 0.4 to 0.6 Mach has a greater impact on the flutter critical velocity, which increases by 12.03%. The greater the aircraft’s flight speed is, the more severe the stiffness affects the wing limit cycle oscillation (LCO) amplitude.

Tian W., Zhao T., Yang Z.

A unified analytical model is developed to investigate the nonlinear aeroelastic behaviors of a supersonic functionally graded piezoelectric material (FGPM) plate with general boundary conditions under electro-thermo-mechanical loads. The formulation is derived by first-order shear deformation theory (FSDT) and supersonic piston theory, and the geometrical nonlinearity is considered based on von Karman large deformation theory. The motion equations of the supersonic FGPM plate are obtained through Hamilton principle and a modified Fourier series with auxiliary functions is employed to satisfy the possible mechanical and electric boundary conditions. Nonlinear aeroelastic responses of the FGPM plate are solved via Newmark integration technique combined with Newton-Raphson iterative scheme. Convergence and comparison studies show that the proposed model has sufficient accuracy in predicting aeroelastic stability and nonlinear dynamic responses as well as possess reliability in handling arbitrary boundary conditions. Numerical examples are carried out to demonstrate that several key parameters can significantly affect flutter and thermal buckling of the plate. Additionally, the effects of thermal and electric loads on limit cycle oscillation and dynamic bifurcation of nonlinear FGPM plate are examined. A higher temperature rise can result in the transition of the system from stable to chaos and more complicated evolution of dynamic motions.

Sun Y., Song Z., Ma W., Li F.

It is well known that lumped masses can change the frequency characteristics of the structural system, and aeroelastic flutter happens due to the coalescence of two modes. Therefore, it can be expected to improve the aeroelastic stability by the lumped mass. This paper studies the influence mechanism of the lumped mass on the aeroelastic behaviors of two-dimensional (2D) panels in supersonic airflow, and proposes an axially functionally graded design method using the lumped mass. In this investigation, the finite element method (FEM) is used to formulate the aeroelastic equation of motion for the panels with the lumped mass and spring constraint. For 2D panels with the lumped mass, the local mode coalescence is observed, and the influences of the weight and location of the lumped mass on the flutter stability and their mechanism are analyzed. The optimal ranges for the weight and location of the lumped mass are given out. For 2D panels with the spring constraint, the sudden decrease of the flutter bound due to the mode veering are analyzed, and an effective method to eliminate it by using the lumped mass is proposed. Finally, a structural optimization method based on the axially functionally graded design is proposed.

Wang Z., Chen H., Wang G., Zhang Y., Zheng C.

In this paper, the critical points of flutter of a composite panel predicted using a finite element model are studied using an eigenvector orientation method. Taking a supersonic simply supported panel and clamped panel models as examples, the accuracy of the eigenvector orientation method for predicting the critical points of flutter is verified, and the misjudgments of “channeling” (modal crossover) and other phenomena by traditional judgment methods are avoided. The piezoelectric actuators are combined with the upper and lower surfaces of the simply supported panel (clamped panel), and the aerodynamic parameters of each finite element are changed by activating the piezoelectric actuators. Based on linear quadratic adjustment theory, an optimal control method for the active flutter suppression is designed. The influence of the activation position of the different piezoelectric actuators on the critical points of flutter is studied to increase the flutter speed to an ideal range. The results show that the control torque generated by the piezoelectric actuators can offset the occurrence of flutter and provide a lead time for possible flutter control.

Starossek U., Starossek R.T.

The eccentric-wing flutter stabilizer is a passive aerodynamic device for raising the flutter speed of a bridge. It consists of wings running parallel to the bridge deck. In contrast to similar devices proposed in the past, the wings do not move relative to the bridge deck and they are positioned outboard the bridge deck to achieve a greater lateral eccentricity. This enables the wings to produce enough aerodynamic damping to effectively raise the flutter speed. A comprehensive parametric flutter analysis study is presented in which both the properties of the bridge and the configuration of the wings are varied. The bridge properties and the wing configuration are each summarized in four non-dimensional quantities. The parameter space within which these numbers are varied are determined on the basis of previous work and the structural properties of actual long-span bridges. As for the wind forces, a streamlined bridge deck contour is assumed. The main interest of this study is the relative flutter speed increase due to the wings. This and other non-dimensional results are presented in diagrams and discussed. Both multi-degree-of-freedom and generalized two-degree-of-freedom flutter analyses are performed. Torsional divergence is addressed. A strategy for choosing a cost-efficient wing configuration is suggested.

Gao C., Liu X., Zhang W.

The variation in the flutter boundary of the AGARD 445.6 wing in transonic and low supersonic states is an unresolved issue in the field of aeroelasticity. This well-known variation phenomenon is m...

Farsadi T., Rahmanian M., Kurtaran H.

In the present study, nonlinear panel flutter and bifurcation behavior of functionally graded ceramic/metal wing-like tapered and skewed plates are investigated. Porosities are distributed over the cross-section of the functionally graded structure. The flutter speed, limit cycle oscillations, and bifurcation diagrams of the functionally graded plate with two types of geometrical non-uniformities being skewness and taperness are explored. Nonlinear structural model is utilized based on the virtual work principle by including the von-Karman nonlinear kinematic strain assumption. The first order shear deformation theory is employed to consider the transverse shear effect in the structural model. First-order linear piston theory is used to model the aerodynamic loading while the generalized differential quadrature method is employed to solve the governing equations of motion. Time integration of the final ordinary equations of motion is carried out using the Newmark average acceleration method. Different volume fractions are investigated to enhance the flutter instability margins and post-flutter behavior of functionally graded plates. Results demonstrate that the volume fraction and porosity coefficients have significant effects on dynamic behavior and limit cycle oscillation amplitudes.

Jia Y., Lu J., Zhao Z., Liu Q., Lv S.

Li J., Zhang X., Song H.

Araujo G.P., da Silva J.A., Marques F.D.

Palakurthy S., Schemmel A., Zope A., Collins E., Bhushan S.

In this report, we investigate the onset of chaotic flutter in laminar and turbulent flows over a two-dimensional semi-infinite panel using time-accurate fluid–structure interaction (FSI) simulations of shock–boundary-layer interactions (SBLIs). Results indicate that the critical dynamic pressure and the nature of the panel dynamics strongly depend on the static pressure differential across the shock, the local loading, the viscous and turbulent damping in the flow, and the formation of dynamic flow separation bubbles due to the SBLIs. The structural system undergoes local instability (Hopf bifurcation) when the local loading due to panel deformation overcomes the static pressure differential across the shock. In the absence of external fluid instabilities, the structural oscillations will induce unsteadiness in the flowfield, resulting in low-frequency limit-cycle oscillations. Viscous and turbulent damping in the boundary layer also delays the bifurcation and reduces the amplitude of the oscillations. Sufficiently strong shocks can produce localized flow separations, which drive additional boundary-layer instabilities, resulting in an early bifurcation. In the presence of external fluid instabilities, the behavior of the FSI strongly depends on the nonlinear coupling of their instabilities. Chaotic oscillations are observed when the fluid instabilities are dominant enough to induce structural oscillations with broadband frequencies.

Moreira J.A., Moleiro F., Araújo A.L., Pagani A.

Moreira J.A., Moleiro F., Araújo A.L., Pagani A.

Tang R., Li D., Wei Y., Li E., You Z.

This study introduces a novel optimization approach for airfoil-based flutter energy harvesters through installation angle adjustment, addressing a critical research gap in the field where previous studies have primarily focused on structural modifications. To investigate this unexplored avenue, we developed a flutter energy harvester with an adjustable installation angle mechanism, aiming to reduce critical flutter velocity, broaden operational bandwidth, and improve energy harvesting efficiency under low-speed airflow conditions. The performance characteristics of the harvester were comprehensively evaluated through both numerical simulations incorporating fluid–structure-electrical coupling and wind tunnel experiments conducted at four distinct installation angles (0°, 3°, 6°, and 9°). The experimental results demonstrated a significant correlation between installation angle and critical flutter velocity, showing a consistent reduction from 7.8 m/s at 0° to 7.2 m/s at 6°, and further decreasing to 6.3 m/s at 9°. Notably, optimal performance was achieved at a moderate installation angle of 3°, yielding a maximum output voltage of 12.0 V and power output of 0.58 mW, which substantially exceeded the baseline performance at 0° (10.9 V, 0.48 mW). However, further increasing the installation angle to 9° led to performance degradation, attributed to a premature aerodynamic stall, resulting in reduced output metrics of 7.9 V and 0.25 mW for voltage and power, respectively. These findings demonstrate a simple yet effective method for enhancing flutter energy harvesting performance in low-speed airflow conditions.

Chwał M.

This paper considers the free vibration and flutter of carbon nanotube (CNT) reinforced nanocomposite plates subjected to supersonic flow. From the literature review, a great deal of research has been conducted on the free vibration and flutter response of high-volume CNT/nanocomposite structures; however, there is little research on the flutter instability of low-volume CNT/nanocomposite structures. In this study, free vibration and flutter analysis of classical CNT/nanocomposite thin plates with aligned and uniformly distributed reinforcement and low CNT volume fraction are performed. The geometry of the CNTs and the definition of the nanocomposite material properties are considered. The nanocomposite properties are estimated based on micromechanical modeling, while the governing relations of the nanocomposite plates are derived according to Kirchhoff’s plate theory with von Karman nonlinear strains. Identification of vibrational modes for nanocomposite thin plates and analytical/graphical evaluation of flutter are presented. The novel contribution of this work is the analysis of the eigenfrequencies and dynamic instabilities of nanocomposite plates with a low fraction of CNTs aligned and uniformly distributed in the polymer matrix. This article is helpful for a comprehensive understanding of the influence of a low-volume fraction and uniform distribution of CNTs and boundary conditions on the dynamic instabilities of nanocomposite plates.

Guo Q., Li X., Zhou Z., Ma D., Wang Y.

Flutter is an extremely significant academic topic in both aerodynamics and aircraft design. Since flutter can cause multiple types of phenomena including bifurcation, period doubling, and chaos, it becomes one of the most unpredictable instability phenomena. The complexity of modeling aeroelasticity of high flexibility wings will be substantially simplified by investigating the prospect of system identification techniques to forecast flutter velocity. Therefore, a novel neural network (NN)-based method for aeroelastic system identification is proposed. The proposed NN-based approach constructs an NN framework of high flexibility wings flutter models with different materials and sizes, which can effectively predict the flutter velocity of flexible wings. The accuracy of the method is demonstrated by comparing with the simulation results.

Vindigni C.R., Mantegna G., Orlando C., Alaimo A., Berci M.

Cao D., Gao C., Zhou X., Zhou Y., Wang J., Guo X.

Advanced aircrafts have incorporated bio-inspired morphing structures to adapt to multienvironment and perform multimission. But it will cause serious issues with structural reliability and aeroelastic stability. This paper studies the critical flutter speed of a morphing wing structure and evaluates the deformation strategies. First, a biomimetic wing is considered as a variable cross-section cantilever beam, and the flutter model with Theodorsen unsteady aerodynamics is theoretically derived. The finite element theory is used to discretize the obtained PDEs with variable coefficients. Second, three typical wing models are examined to verify the model’s accuracy against finite element simulation findings for modal frequencies and critical flutter speeds. The results indicate good agreement, with errors of less than 3% for modal frequencies and fewer than 2.1% for critical flutter speeds. Thirdly, the flutter wind speeds are examined to assess the aeroelasticity properties for three different morphing strategies of biomimetic wing structures. The findings show that both forward bending of the elastic axis and greater density concentration near the wing root increase flutter speed. And the density distribution has a smaller effect on flutter speed than elastic axis bending. When it comes to static aeroelasticity, excessive folding ratios cause divergence problems.

Pan D., Xing Y.

According to the Donnell–Mushtari shell theory, this work presents a closed-form solution procedure for free vibration of open laminated circular cylindrical shells with arbitrary homogeneous boundary conditions (BCs). The governing differential equations of free vibration are derived from the Rayleigh quotient and solved by the iterative separation-of-variable (iSOV) method. In addition, considering axial aerodynamic pressure, simulated by the linear piston theory, the exact eigensolutions for the flutter of open laminated cylindrical shells with simply supported circumferential edges and closed laminated cylindrical shells are also achieved. The governing differential equations of cylindrical shell flutter are derived from the Hamilton variational principle and solved by the separation-of-variable (SOV) method. The influence of circumferential dimension on flutter speed is investigated for open cylindrical shells, which reveals that the number of circumferential waves in critical flutter mode increases with circumferential length, and there exists an infimum for flutter speed that is an invariant independent of circumferential length. The present results agree well with those obtained by the Galerkin method, the finite element method, and other analytical methods.

Nie G., Li H., Chen X.

Variable Angle Tows (VAT) composite materials can effectively transfer major stresses from the interior region to the edges through in-plane load redistribution, thereby significantly enhancing their structural performance. Therefore, correct handling of boundary conditions is crucial in analyzing VAT structures. Considering that most practical engineering cases involve non-ideal or non-classical boundary support, this paper proposes an efficient method to address the nonlinear thermal flutter problem of elastic supported VAT curved panels in supersonic airflow. Assuming the fiber orientation angle varies in four different ways along the x-direction, the basic equations are established based on the von Kármán large deformation plate theory and the first-order piston theory. The generalized Galerkin method, capable of handling arbitrary elastic boundary constraints, is used to solve the problem in the space domain, while the Runge-Kutta method is applied in the time domain. Numerical examples illustrate how elastically restrained conditions, fiber orientation angles, height-rise ratio, and thermal loads, along with aerodynamic pressure, influence flutter responses of VAT panels. The presented method can be used for the aeroelastic stability design of VAT curved panels under arbitrary boundary conditions.

Dilmi S.

Kılıçarslan D., Kösterit G., Cigeroglu E.

Flutter instability occurs when the modal damping of the system becomes negative while the natural frequency is nonzero, in which the energy of the system increases while the structure is undergoing vibrations. As an aeroelastic problem, flutter occurs when wing-like or panel structures undergo self-excited vibrations where the vibration amplitude increases greatly while the fluid flow speed is at or higher than a critical threshold. Structural system is generally modeled using finite element or the Rayleigh-Ritz method; one other alternative is the generalized differential quadrature method (GDQM), where the derivative in the domain is approximated by the function values in the domain. In this work, the aeroelastic flutter problem of simply supported and cantilever plates under supersonic flow is modeled using linear Kirchhoff-Love plate theory and first-order piston theory to model the fluid-structure interaction. Equation of motion is discretized using GDQM in the spatial domain to transform differential equations into algebraic equations. Resulting algebraic equations are solved as a state space eigenvalue problem to obtain complex mode shapes and complex eigenvalues. Results are compared with those found in the literature, and the ability of GDQM to be applied to aeroelastic flutter analysis is assessed.