Mutual interactions-between aerodynamic and structural forces cause aeroelasticity that is very important in aircraft Wings. In this paper, instability of a Wing in dynamic situation that is called Flutter is considered for a composite Wing in subsonic flows. The "Strip Theory" approach is used to calculate the aerodynamic forces along the Wing. For this reason, displacements along the Wing and Flutter speed are determined using the "Assumed Mode Method ". In this method, the displacement along the Wing is assumed by definite boundary conditions. The stored potential and kinetic energy in the Wing, as well as the generalized aerodynamic forces and moments on the Wing, are determined. By employing Lagrange’s equations, the Wing motion is formulated. A Computer program has been developed to calculate the speed of the Wing instability, the effects of the elastic axis and the center of gravity has been investigated on the stability of the Wing. The Flutter speed is calculated for a certain Wing, which the data is available, and a suitable elastic axis has been determined for a specified center of gravity.

This study addresses the prediction of the Flutter speed for a double-sweep folding Wing in subsonic airflow, an area less explored in past research. Two types of modeling are employed: structural and aerodynamic. The structural model treats the Wing as an Euler-Bernoulli beam. For the aerodynamic model, Theodorsen's unsteady aerodynamic theory is used. This theory is initially in the frequency domain but is converted to the time domain using the Kussner function and a new formulation method. Kinetic energy, strain energy, and the work of aerodynamic forces are then calculated. The differential equations governing the Wing structure are derived using Hamilton's principle. The Wing's motion equation is obtained using assumed modes and the Galerkin method. The instability Flutter speed is determined through the p-method, and graphs of frequency versus airflow velocity are plotted. The results indicate that using the Kussner function for variable airflow improves the accuracy of Flutter speed prediction. The analysis of sweep angle changes on Flutter speed and frequency revealed that sweep angle one has the least positive effect, while sweep angle two has the most positive effect on Flutter speed and frequency, respectively.

In aircraft with flexible high aspect ratio Wings, it is possible to couple flight dynamics modes and aeroelasticity. This coupling can lead to the body-freedom Flutter (BFF) phenomenon, which is the subject of this article. In this study, the planar flight dynamics assumption and the model of a complete aircraft with flexible Wings have been used. In this type of aircraft, due to the high aspect ratio of the Wings, the effects of nonlinear terms on the dynamic response of the aircraft cannot be ignored. Therefore, for modeling the structure, the generalized nonlinear flexible Euler-Bernoulli beam model with bending-bending-torsion degrees of freedom and for modeling the aerodynamics, the Wagner function with the static stall model has been used. Using the developed model, the nonlinear behavior of the Wing and the aircraft due to the occurrence of the BFF and Wing Flutter (WF) is studied. Also, a sensitivity analysis for the BFF is done and post-instability limit cycle oscillations and subcritical behaviors are investigated.

In this paper, the Flutter analysis of an aircraft Wing carrying, elastically, an external store is studied. The Wing is considered as a uniform cantilever beam and the external mass is connected to the Wing by one spring and damper. The aeroelastic partial governing equations are determined via Hamilton’s variational principle. Also, modified Peter's finite-state aerodynamic model is employed. The resulting partial differential equations are transformed into a set of ordinary differential equations through the assume mode method. Effects of different situations like the Wing without external mass, the Wing with a rigidly attached external mass, and the Wing with an elastically attached external mass on the Flutter speed and frequency are investigated. The numerical results for a Wing are compared with published results and good agreement is observed. Then, simulation results for the Wing with an elastically attached external mass are presented to show the effects of the Wing sweep angle, store mass and its location and the spring rigidity constant on the Wing Flutter. Results show that sliding the external mass toward the Wing tip in spanwise direction and also toward the trailing edge in chordwise direction decreases the Flutter speed. Furthermore, increasing the store mass and spring constant decreases the Wing Flutter speed. Results show that increasing the Wing sweep angle increases the Flutter speed, in all situations.

In this study, Flutter of functionally graded carbon nanotube (FG-CNT)-reinforced composite Wing carrying a distributed patch mass is analyzed and presented. Wing is modeled by a rectangular plate with cantilever boundary conditions in supersonic flow. To evaluate the displacement fields of the moderately thick plate, First-order shear deformation theory (FSDT) and chebyshev polynomials series are applied. In supersonic airflow simulation effect, the firstorder piston theory was used and differential equation governing the system was adapted, using the Hamilton principle. In this study, 4 different types of CNT are considered through the thickness. CNT distribution patterns are as uniform, decreasing, decreasing-increasing, and increasing-decreasing. Finally, the effects of size, mass, and location of the distributed patch mass as well as various CNT distributions and fiber orientation angle in a two-layer antisymmetric composite on Flutter boundaries were studies. In comparisons with the results of previous studies, a good agreement is observed. The results showed that the Flutter boundary reduced with increasing mass ratio and increased in longer length of added mass. By increasing orientation’ s angle of CNT fiber of anti-symmetric composite, the Flutter boundary is raised and has different behavior for different distribution patterns.

The main goal of this article is to analyze the sensitivity and find the most effective property among structural properties that have the most significant impact on the Flutter velocity of a composite Wing. For this purpose, the corresponding Aeroelastic equations of a composite Wing have been derived using the Euler-Bernoulli beam model and discretized by the Galerkin method. Based on Jones's unsteady aerodynamic model, aerodynamic loads have been incorporated into the aeroelastic model. Then, Flutter velocity was determined through eigenvalue analysis of the obtained aeroelastic equations. The Flutter velocity changes with a specific interval of each input. With the help of reverse engineering, the effects of structural properties (including material properties and effective stiffness) and their sensitivity were determined. The results show that the Torsional Effective Stiffness has the most significant effect and high sensitivity on Flutter velocity. In this work, other parameters (including flow properties, Wing geometry, and airfoil) are assumed to be unchangeable. The geometry of the Wing is considered rectangular and straight.

Aeroelasticity is the major source of various forms of instability in aircraft. For this reason. considering the effects of this phenomenon in design of airframe structures is essential. From various forms of instability. self-excitation vibration of Wing which is called Flutter is very important.The goal of this research is study of bending-torsion Flutter of a Wing of a full composite aircraft based on Joint aviation Requirements (JAR23). For this reason. it must be shown that the natural frequencies of bending and tensional vibration of the Wing arc differ from each other. For achieving this goal a finite element software (NISA) is used.Two models of Wing. based on lumped and consistent approaches arc made. To show thevalidity of the consistent model. a convergence analysis is performed. To verify the results obtained from the models. they are compared with an approximated solution after this step. flexural stiftiless. tensional stifti1ess and mass distribution along the frequenccies of the Wing are obtained from the finite element model. In the next step. the frequencies of torsional and bending vibration of the Wing are calculated by the lumped and consistent models and compared with each other.Finally based on JAR23 standard and the results obtained from the models. it is Concluded that there is no Flutter for the Wing of the full composite aircraft in the range of design speed.

The main goal of this article is to study the Wing bending - aileron rotation Flutter of a full composite aircraft, based on Joint Aviation Requirements (JAR23).For this Reason, it must be shown that the frequency of vibration of Wing under bending is different from that of the rotation vibration of the aileron. In this way, one item of JAR23 standard can be satisfied.To simulate the physical behavior of the Wing and the aileron, a finite element software (NISA) is used. Also, an experimental modal analysis technique is used to validate the results obtained from the model. After making the finite element models, convergence analysis is performed to validate them. The natural frequency of the aileron is calculated by the finite element software by experimental modal analysis tool.To validate the numerical result, the results obtained from the model are compared with the experimental data obtained from the testes. In the first step, by applying displacement boundary conditions on the model, natural frequency of the aileron under rotational is calculated, Finally, based on JAR23 standard and the results obtained from the model and experiments, it is concluded that the aircraft is free from Wing bending - aileron rotation Flutter.

Flutter and limit cycle oscillations (LCO) control of a structural non-linear Wing with actuator saturation is considered in this paper. For this purpose composite nonlinear feedback (CNF) theory is used The CNF theory accounts for the effect of actuator saturation and here it can be shown, this control method can effectively suppress the Flutter and LCO of a structural nonlinear Wing with constrained input. The aeroelastic model is a low aspect ratio rectangular Wing in a low subsonic flow with structural nonlinearities. The structural nonlinearity arises from double bending in both chord-wise and span-wise directions (Von Karman plate theory). For aerodynamics modeling a full and reduced order aerodynamics model based on the modified vortex lattice method is used Results from simulations show, with this simple controller, we can effectively suppress LCO and extend Flutter boundary.

The body freedom Flutter phenomenon is one of the aeroelastic instabilities that occurs due to the coupling of the aeroelastic bending mode of the Wing with the short-period mode in the flight dynamics of the aircraft. By using the aeroservoelastic model and applying closed loop control, this phenomenon can be suppressed in the operating conditions of the aircraft and the velocity of this event can be increased. The simplest model aircraft capable of displaying this instability includes the flexible Wing and the planar flight dynamics model. For this purpose, the Wing structure is modeled using the Euler-Bernoulli beam and, the theory of minimum variable state is used to model unstable aerodynamics to make the conditions suitable for modeling the system in state space. In the control section, the elevator is used as the control surface and LQR theory with Kalman filter is used to body freedom Flutter suppression. Finally, the effect of adding a closed loop control to increase the body freedom Flutter velocity and the limitations of this work are studied.