Sharif Digital Repository

This paper presents a method for nonlinear aeroelastic analysis of a Human Powered Aircraft (HPA) wings. In these types of aircrafts there is a long wing with high flexibility. Wing flexibility coupled with the long span leads to the possibility of the large deflections during normal flight operation, so, nonlinear modal analysis technique is used for structural modeling. Unsteady linear aerodynamic theory is used for determination of aerodynamic loading on the wing (linear aerodynamics and nonlinear structure). Combining these two types of formulation yields a nonlinear aeroelastic model. Mode summation techniques along with Galerkin's method are used to determine the governing equations of... 

In this paper, the aeroelastic behavior and flutter instability of aircraft wings in subsonic incompressible flight speed regime are investigated. Quasi-steady and unsteady aerodynamic models are used for aerodynamic modeling and the obtained aeroelastic predictions are compared to those available in the specialized literature. Based on a number of test cases, it is shown that the quasi-steady aerodynamic models are inadequate for the determination of aeroelastic behavior and flutter boundary of aircraft wings in the incompressible flight speed range. © 2006 Elsevier Ltd. All rights reserved  

The subject of the present paper is the investigation of the sharp edged gust effects on the aeroelastic behavior of a flexible wing. It is important to determine the response of the wing to the atmospheric turbulences during normal flight. So, linear modal analysis technique and linear quasi-steady aerodynamic are used for structural modeling and aerodynamic loading, respectively. Also, Lagrange method is used to obtain the system of equations of motion. Using the normal modes of free vibration, structural and aerodynamic matrices can be constructed. Then the aeroelastic instability of the system is determined using p method. Kussner function is used to model the sharp gust effects on the... 

The nonlinear aeroelastic behavior of a three-dimensional general laminated composite plate at high supersonic Mach numbers is investigated using von Karman's large deflection plate theory and quasisteady aerodynamic theory. Galerkin's method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Nonlinear flutter results are presented with the effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping  

In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the... 

Flutter of cantilevered, functionally graded cylindrical shells under an end axial follower force is addressed. The material properties are assumed to be graded along the thickness direction according to a simple power law. Using the Hamilton principle, the governing equations of motion are derived based on the first-order shear deformation theory. The stability analysis is carried out using the extended Galerkin method and minimum flutter loads and corresponding circumferential mode numbers are obtained for different volume fractions, length-to-radius, and thicknesses-to-radius ratios. Two different configurations are considered for the FGM: one in which the metal phase is the outer layer... 

Stability analysis of a horizontal cantilevered pipe conveying fluid with an inclined terminal nozzle is considered in this paper. The pipe is modelled as a cantilevered Euler-Bernoulli beam, and the flow-induced inertia, Coriolis and centrifugal forces along the pipe as well as the follower force induced by the jet-flow are taken into account. The governing equations of the coupled bending-torsional vibrations of the pipe are obtained using extended Hamilton's principle and are then discretized via the Galerkin method. The resulting eigenvalue problem is then solved, and several cases are examined to determine the effect of nozzle inclination angle, nozzle aspect ratio, mass ratio and... 

The aeroelastic flutter characteristics of a functionally graded carbon nanotube reinforced composite (FG-CNTRC) truncated conical shell under simultaneous actions of a hydrostatic pressure and yawed supersonic airflow are scrutinized. The nonlinearity in geometry of the conical shell is considered in Green–Lagrange sense and the model is derived according to the Novozhilov nonlinear shell theory. The aerodynamic pressure is modeled based on the quasi-steady Krumhaar's modified supersonic piston theory by considering the effect of the panel curvature and flow yaw angle. Parametric studies are conducted to investigate the effects of boundary conditions, semi-vertex angle, distribution and... 

The aero-thermo-elastic stability of layered cylindrical shells with viscoelstic cores is investigated. The Donnell's shell theory for the outer layers and the first order shear deformation theory for the viscoelastic layer are employed in conjunction with the von Karman-Donnell kinematic nonlinearity to construct the model. The pre-stresses and pre-deformations arisen from the temperature rise and static aerodynamic pressure are first determined by solving the nonlinear thermo-elastic equilibrium equations using by an exact analytical method. The results are then used in the linear aeroelastic stability equations and analyzed with the Galerkin's procedure to determine the supersonic flutter... 

In this paper, the effects of different parameters on the nonlinear aeroelastic behavior of functionally graded flat plates are investigated. Considering the through-the-thickness continuous variation of the material properties, a combination of the simple rule of mixtures and the Mori-Tanaka scheme is used for estimating the effective properties at each point. The von-Karman large strains and the piston theory are used to model the structural nonlinearity and aerodynamic loading, respectively. By Hamilton's principle the governing nonlinear partial differential equations of motion are derived and then converted to a set of nonlinear ordinary differential equations using the Galerkin method.... 

The supersonic flutter analysis of simply supported FG cylindrical shell for different sets of in-plane boundary conditions is performed. The aeroelastic equations of motion are constructed using Love's shell theory and von Karman-Donnell-type of kinematic nonlinearity coupled with linearized first-order potential (piston) theory. The material properties are assumed to be temperature-dependant and graded across the thickness of the shell according to a simple power law. The temperature distribution is assumed to vary in the thickness direction and is obtained by solving the steady-state heat conduction equation. The pre-stresses due to the thermal and mechanical loadings are obtained by... 

In this paper, the nonlinear aeroelastic behavior of functionally graded plates is studied in supersonic flow. For this purpose, the von Karman strains and piston theory have been employed to model structural nonlinearity and quasi-steady aerodynamic panel loading, respectively. The material properties of the plate are assumed to be graded continuously in the direction of thickness. The variation of the properties follows a simple power-law distribution in terms of the volume fractions of constituents. The Hamilton's principle is used to construct the coupled nonlinear partial differential equations of motion. The derived equations are transformed into a set of coupled ordinary differential... 

This paper presents an analytical method in computational aeroelasticity for an airfoil considering two degrees of freedom (heaving and pitching) based on the Wagner integral function. In the obtained aeroelastic equations of motion, there are some integral parts that give an integro-differential system of equations. Using appropriate approximation for the Wagner function, a new form of equations can be obtained by derivation from mentioned equations. These equations are in the form of ordinary differential equations. Using the obtained equations, the flutter speed is predicted for a given airfoil and the results are compared with the results of other investigators. Also, the dynamic... 

In aircraft wings, aileron mass parameter presents a tremendous effect on the velocity and frequency of the flutter problem. For that purpose, we present the optimization of a composite design wing with an aileron, using machine-learning approach. Mass properties and its distribution have a great influence on the multi-variate optimization procedure, based on speed and frequency of flutter. First, flutter speed was obtained to estimate aileron impact. Additionally mass-equilibrated and other features were investigated. It can deduced that changing the position and mass properties of the aileron are tangible following the speed and frequency of the wing flutter. Based on the proposed... 

The problem of nonlinear aeroelasticity of a general laminated composite plate in supersonic air flow is examined. The classical plate theory along with the von-Karman nonlinear strains is used for structural modeling, and linear piston theory is used for aerodynamic modeling. The coupled partial differential equations of motion are derived by use of Hamilton's principle and Galerkin's method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping on the nonlinear aeroelastic... 

This paper presents a coupled flap-lag-torsion aeroelastic stability analysis and response of a hingeless helicopter blade in the hovering flight condition. The boundary element method based on the wake eigenvalues is used for the prediction of unsteady airloads of the rotor blade. The aeroelastic equations of motion of the rotor blade are derived by Galerkin's method. To obtain the aeroelastic stability and response, the governing nonlinear equations of motion are linearized about the nonlinear steady equilibrium positions using small perturbation theory. The equilibrium deflections are calculated through the iterative Newton-Raphson method. Numerical results comprising steady equilibrium... 

In this article, analysis of supersonic flutter of functionally graded open conical shell panels with clamped and simply supported edges is presented. The aeroelastic stability problem is formulated based on first-order shear deformation theory as well as classical shell theory and solved using Galerkin method. The effects of the volume fractions of constituent materials, the semi-vertex and subtended angles, thickness, and length on the flutter of the functionally graded conical shell panel are investigated. It is shown that the discrepancies between the results of the present classical shell theory and first-order shear deformation theory for the critical aerodynamic pressure are generally... 

This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli... 

Supersonic aeroelastic instability of a three-layered sandwich beam of rectangular cross section with an adaptive magneto-rheological fluid (MRF) core layer is investigated. The panel is excited by an airflow along it's longitudinal direction. The problem formulation is based on classical beam theory for the face layers, magnetic field dependent complex modulus approach for viscoelastic material model and the linear first-order piston theory for aerodynamic pressure. The classical Hamilton's principle and the assumed mode method are used to set up the equations of motion. The validity of the derived formulation is confirmed through comparison with the available results in the literature. The... 

In this paper, the dynamic instability of a nonlinear system has been studied using the stochastic vibration analysis and employing statistical properties of the system response. In this method neither the time domain analysis nor limit cycle oscillations were used. A two degrees-of-freedom airfoil subjected to an aerodynamic quasi-steady flow with a nonlinear torsional spring was considered as the case study. The spring nonlinearity was examined in hardening and softening states. A random force in the form of the white noise with Gaussian function was added to the aerodynamic lift force. The statistical linearization and random vibration analysis were applied to the nonlinear system to...