Mean axes provide the usual reference in maneuvering and dynamic response analyses of flexible vehicles. Attached or structural axes have also been used because the flexibility characteristics of the structure are only determined for a restrained structure. If the structural axes are employed, a relationship is required for the orientations of the structural axes relative to the mean axes, since the equations of motion determine the orientations of the mean axes. If this relationship is not considered, as it has not been in a number of publications, the solution to the equations of motion of the structural axes is not invariant with the choice of support configuration used in the calculation of the structural flexibility influence coefficients and is, therefore, incorrect. This relationship and the correct equations of motion for the structural axes are presented, and the correctness of the formulation is demonstrated numerically in studies of longitudinal maneuvering of an example forward-swept-wing airplane at constant forward velocity. Although the paper assumes constant airspeed in the basic developments, it concludes with discussions of aeroelastic speed derivatives and aeroelastic effects on drag. The paper assumes quasisteady equilibrium of the structure with its applied loads throughout.

Equations of motion of a quasisteady flight vehicle utilizing restrained static aeroelastic characteristics

A finite-element method, with sources and doublets representing the body and vortex-lattice representing lifting surfaces, has been developed for calculating both the longitudinal and the lateral aerodynamic coefficients of a subsonic airplane. This method has been verified with the wind-tunnel test data. 6 A a ft F I" F" xc XL XC.G. £ R RB2 d d2 (Dx,Dy, Nomenclature = twist angle = dihedral = sweep angle = angle of attack = sideslip angle = Mach number = pertubation potential of source = pertubation potential of doublet = vortex strength = source strength = doublet strength = position vector = position vector of control point — position vector of load point = position vector of airplane e.g. = position vector of source or doublet (JCC3

A finite-element method for calculating aerodynamic coefficients of a subsonic airplane.

Mechanical Engineering) The Effect of Wing Damage on Aeroelastic Behavior by Howard J. Conyers Department of Mechanical Engineering and Materials Science Duke University

/pdf/the-effect-of-wing-damage-on-aeroelastic-behavior-2lje6cebnn.pdf

The Effect of Wing Damage on Aeroelastic Behavior

Equations of motion of an elastic flight vehicle utilizing static aeroelastic characteristics of the restrained vehicle

: The simulation of modern aircraft with lightweight structures and high bandwidth control systems requires more sophisticated modeling than the standard six degree-of-freedom representation. The objective of this work was to investigate and test methods for incorporating longitudinal structural mode vibration data into the simulation equations which would allow for variation in frequency and shape functions relative to an established baseline. Using a two-dimensional COSMOS/M(TM) finite element model, the thickness and the length of the aircraft model were varied to match the resonant frequency of the baseline model. The addition of forces then matched the mode shape of the computer model to the actual shape of the baseline. The results, confirmed by experimental tests, indicated that it is possible to effectively model the natural frequency and mode shape at any longitudinal location as center of gravity and/or weight is varied about a nominal condition. Moreover, the methodology allows new configuration baselines to be established by the matching of modal frequencies and shapes to external data from ground or flight tests.

http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA383217&Location=U2&doc=GetTRDoc.pdf

Investigation of Dynamic Structural Models Suitable for the Simulation of Large Aircraft

Aerodynamic and structural influence coefficients are utilized to determine the load distributions, deflections, and trim parameters for a vehicle in quasi-static aeroelastic equilibrium. A matrix formulation is used to solve the various quasi-static aeroelastic problems. Nonlinearities in the aeroelastic trim equations are accounted for by an iteration of the classical closed form solution. Aerodynamic and structural idealizations are related by a surface spline transformation. Solutions are developed for symmetric, antisymmetric, and asymmetric load conditions on symmetric vehicles of general geometric shapes which may include both lifting surfaces and lifting bodies. INTRODUCTION With the advent of large order matrix solutions for the analysis of complex structures a need has arisen for a complementary approach to the external loads problem. Finite element structural analysis techniques demand that the external loads be distributed over the structure at discrete points. Therefore, shear, moment, and torque distributions along a psuedoelastic axis are no longer sufficient to define the external load distributions required by the stress analysis. A general finite element approach to the problem of the determination of aeroelastic loads on a flexible vehicle flying in a state of quasi-static equilibrium is presented here. The vector point loads available from this solution are directly applicable to matrix structural analyses. Structural and aerodynamic influence coefficients obtained from finite element idealizations of the aircraft are utilized as a basis for the method. The technique is primarily an extension of the method first suggested by ~ e d m a n ( l ) * and later generalized by odde en.(^) This work extends the efforts of the above-mentioned authors by * Numbers in parentheses designate References at end of paper.

Jack C. Rowan

Papers

Aeroelastic Loads Predictions using Finite Element Aerodynamics

Aeroelastic loads predictions using finite element aerodynamics

Comment on "A Finite-Element Method for Calculating Aerodynamic Coefficients of a Subsonic Airplane"