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In this paper linear aeroelastic analysis of a swept wing with two degrees of freedom in an incompressible flow is investigated in time - domain. The equations of the motion of an elastic wing are derived from Lagrange’s equations in time - domain. The wing is modeled as a cantilever beam rigidly connected to the root. Considering assumed modes of cantilever beam, aerodynamic forces and moments acting on the wing are derived using strip - theory in an unsteady incompressible potential fluid flow. The governing aeroelastic equations of the system have been introduced in dimensionless form. These equations are solved via a numerical method. Comparisons between obtained results and both available experimental data and the results of some cited references indicate a close agreement.

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A new complete system model of a flapping wing has been derived which consists of all effective parameters. Flapping mechanism can deliver maneuverability as well as low speed flight capability in MAVs. Here a validated aeroelastic model is being developed based on the wing torsional deformation assumption. Based on the proposed model complete parameter study could be performed and consequently the optimization requirements can be extracted. Experimental results of a static test stand have been used for validation. Performance indices, composed of force generated, power consumption and efficiency are depicted in terms of stiffness and kinematic properties. The average behavior is being referred. It is revealed that by changing frequency and speed, the optimum values for stiffness and amplitude are independent. Therefore using suitable kinematics one can utilize specified constant stiffness to optimize the flapping robot flight.

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In this paper flutter phenomena for a cropped wing with an external store using numerical and experimental methods in a subsonic and incompressible flight regime has been studied. Wing structure was modeled base on von Karman plate theory. A 3D time domain unsteady vortex lattice method was used for wing aerodynamic model and a slender body aerodynamic theory was used for store aerodynamic model. Finally, the aeroelastic governing equations with considering vibratory wing motion has been solved. The experimental tests were performed in an incompressible subsonic wind tunnel. Comparison of experimental results with theoretical analysis shows good agreement with each other especially in calculation of aeroelastic behavior of the wing. In continue, the effects of some parameters such as wing thickness, wing aspect ratio, store position, weight of the store, aerodynamic of the store, store vertical distance from under wing, and center of mass of the store on both flutter speed and instability boundary of the wing have been studied analytically and experimentally. The results show with both increasing aspect ratio and decreasing wing thickness, flutter speed will be decreased. Moreover, change in store position effects on flutter speed of the wing/store configuration. Aerodynamic of the store has no significant effect on flutter speed of the wing/store configuration and increasing store weight leads to increasing flutter speed. Change in center of mass of the store influences on flutter speed.

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In this article the composite wing aeroelastic instability speed is optimized by genetic algorithm relative to fiber angle for different layers and follower forces. Aircraft wing is modeled as a beam with two degrees of freedom, which is a cantilever, with thrust as a follower force and mass of the engine. For structural modeling of composite wing the layer theory has been used and unsteady flow assuming subsonic and incompressible flow has been used for aerodynamic model in the time domain. Using the assumed mode the wing dynamic equations of the motion have been derived by Lagrange equations. Linear flutter speed according to the eigenvalues of the motion equations has been calculated. The process of flutter speed calculation has been converted to computer code in which the number of layers, angle of fibers in each layer, the mass of the engine, and the thrust are input variables and the flutter speed is its output. Using Genetic Algorithm, optimum flutter speed has been obtained by changing the angle of fibers. Finally, the impact of the number of layers, the mass of the engine, and thrust on optimum flutter speed has been investigated.

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Wind turbines are subject to various unsteady aerodynamic effects. This includes the wind gust and the change of wind direction. In this work, the aeroelastic behavior of a reference horizontal axis wind turbine has been investigated under different wind gusts and yaw conditions. Unsteady blade element momentum (UBEM) theory and Euler-Bernoulli beam assumption were used to rotor power estimations. To take into account the time delay in aerodynamic loads due to a sudden change in inflow conditions, a dynamic wake model was implemented. The ONERA dynamic stall model was coupled into the BEM theory to improve the aerodynamic loads prediction in the unsteady inflow and yaw conditions. To verify this method, the results in the case of steady-state are compared with the NREL 5 MW wind turbine and in the unsteady case are compared with the Tjaereborg test turbine. The results indicate that sudden change in wind speed causes sharp fluctuations in terms of elastic torsion of the blade and other parameters such as rotor power. Increasing in wind gradient can leads to increasing time delay to a new equilibrium. The increase in yaw angle can be contributed to the rotor power and the periodic loads reduction. The method presented here may facilitate improvements in the controller design for wind turbines.

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Precise modeling has great importance in systems which are designed to work in transonic regions. The scope of current investigation includes numerical simulation of static aeroelastic phenomena of deformable structures in transonic regimes. Transonic flow brings lots of instabilities for aerodynamic systems. These instabilities bring nonlinearity in flow and structure solvers. Due to improvements in numerical methods and also enhancement in computing technologies, computational costs reduced and high-fidelity simulations are more applicable. Simulations in this paper are done in transonic flow (M = 0.96) on the benchmark wing AGARD 445.6. The procedure includes modal analysis, steady flow simulation and investigation of structure’s elastic behavior. At the first phase, the geometry model is validated by modal analysis with regards to comparison of first four natural frequencies and corresponding mode shapes. Then, a loose or staggered coupling is used to analyze aeroelastic behavior of the wing. In each simulation step, imposed pressure on the surfaces of the wing caused by transonic flow regime, deforms the structure. In the results section, a comparison between imposed pressure coefficients in each step with the existing literature and experimental results are reported. Also, pressure coefficients in each steps are calculated and reported. In this investigation by using multiple steps in one-way fluid-structure analysis, deformations are reduced in each step and as a result, the structure reached its static stability point.

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In this article the vibration analysis of a viscoelastic cantilever beam with piezoelectric layers under aeroelastic force and base excitation is investigated. The beam viscoelastic material is assumed to obey the Kelvin-Voight model. Also the piezoelectric layers are located at the top and bottom beam surfaces with series connections. The aeroelastic force based on piston theory is considered to act as an external force on the beam and also the base excitation is assumed to be random. In this research the cantilever beam with two piezoelectric layers are considered as a mechanism to harvest the bending vibration energy. First, the Galerkin method is used to convert the governing partial differential equation into a set of ordinary differential equations. Then the resulted nonlinear ordinary differential equation coupled with electrical circuit equation of piezoelectric layer are solved numerically by Rung-Kutta method. Finally, by analyzing the response of the governing equations, the influence of the system parameters on the vibration behavior of beam and output voltage are discussed. Results show that the increase of fluid velocity increases vibrational energy system which leads to increase of both vibration amplitude and output voltage. In addition, it was shown that structural damping has a significant impact on the output voltage.

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The flow induced vibration in transonic turbomachines is an important and challenging issue in this field. Blades aeroelastic behavior, in addition to the aeroelastic instability, can leads to blades failure, flow instability and reduce efficiency of the system. Aerodynamic behavior of the system should be investigated prior to aeroelastic study. The purpose of this article is an investigation of aeroelastic instability and behavior of a selected turbomachine. For this purpose, transonic flow in Nasa 37 rotor is simulated and verified using CFX software. Then, rotor blade aeroelastic stability is investigated in three operating points; design, near stall and stall using blade forced vibration in the specified inter blade phase angle (IBPA). In order to reduce grid points and consequently, computational time, phase-lagged boundary condition and fourier transformation method is used. Also, in this research, the algorithm of simultaneous structure-fluid grid generation and the solution algorithm of force vibration structure-fluid interaction of turbomachines is codified and introduced in detail. Employment of fourier transformation method in CFX software for aeroelastic simulation is another innovation of this article. The value of the critical inter blade phase angle which is independent from rotor operational conditions, is obtained in the present research. Aeroelastic simulations show aeroelastic instability of Nasa 37 rotor in the stall condition. In this condition, flow entropy is increased rapidly relative to the design and near stall condition. The blade pressure side has more important role in stall aeroelastic instability and needs further attention in re-design phase.

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The numerical simulation of near-stall condition in a passage of an isolated subsonic rotor is studied in detail. The requirements of numerical simulation in order to resolve turbulent spectra around the blade are studied. According to the fact that most of unsteady aerodynamic phenomena incept from blades leading edge, and the role of this part in types and intensity of instabilities, the goal of this paper is to investigate the effects of changes in radius of leading edge of airfoil on flow phenomena in different scales of wave numbers. The governing equations of flow-field are solved using different numerical approaches. Resolution characteristics of different modeling and simulation techniques are investigated. The primary geometry of blade uses a standard NACA-65 series airfoil, which has been tolerated by 50% variation in circular leading edge radius. Mesh requirements of flow simulation for intended purposes are studied in detail and some recommendations are proposed to be implemented in numerical aeroelastic simulations. Accuracy and fidelity of LES results are studied with extraction of power spectra around the blade and the portion of resolved energy is also estimated. Results suggest that the order of accuracy and grid density highly affect the small-scale flow phenomena. The variations in leading edge radius also have great effect on energy distribution among resolved scales.

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In this paper, we investigate the aeroelastic behavior of double-sweep metal and symmetric composite layup wings. Various strategies have been proposed to suppuration of instability such as using the composite materials in structure. The wing is considered as a cantilever beam with 3 degrees of freedom of bending/ bending/ torsional. For aerodynamic modeling, the quasi-steady and unsteady flow theory in the time domain is used based on the Wagner function and the process of calculation of the flutter velocity is provided in form of software code. Finally, the effect of the ratio of length of the isotropic on the total length of the wing as well as the swept angle of the composite section on the flutter speed have been investigated. The results show that with increasing the length of ratio of the metal part to the total length up to 0.9, the speed of instability increases and after that position, it decreases. Also, negative sweep angle of the swept part of wing increases the speed of instability than the positive sweep angle of the composite part. The results show the best angle of fiber is 30 degrees in range of negative sweep angle, having the highest speed of instability. Also, studies show that with increasing the negative sweep angle from -90 to 0 degrees at different angles of fiber, the speed of instability decreases till to -20 degrees of sweep angle and, then, increases slightly. With increasing the sweep angle from 0 to 80 degrees at different angles of fiber, the speed of instability decreases.
 

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In this study, we derived the rotating airfoil system of equation considering Loewy aerodynamics. To this end, we define the local coordinate system on airfoil and reference coordinate on the hub. We define the free air velocity vector and the airfoil rotating speed vector according to the reference coordinate. So, the Kinetic and Potential energies are derived based on linear stiffness and linear damping according to the Hamiltonian principle. Wakes behind the rotating blades form into the helix. Therefore, we the equation of motion with Loewy aerodynamic which compensates the wake effects. Stability analysis is performed by the well-known P-K method. Flutter speed and stability boundary are estimated. Comparing the results of stability analysis and the reference validates the applied method. Furthermore, we proposed the PID Control to suppress the flutter speed. the PID controller input and command. The desired time and error tolerance are selected to design PID controller. Unit step response shows that pitch angle response is under-damped. However, step response tracks input well. Besides, disturbance rejection by considering the gain from input to output to remain below the gain value is analyzed. 

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