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NASA NTRS1977

Aeroelastic analysis and ground vibration survey of the NASA, Grumman American Yankee modified for spin testing

A complete ground vibration and aeroelastic analysis was made of a modified version of the Grumman American Yankee. The aircraft had been modified for four empennage configurations, a wing boom was added, a spin chute installed and provisions included for large masses in the wing tip to vary the lateral and directional inertia. Other minor changes were made which have much less influence on the flutter and vibrations. Neither static divergence nor aileron reversal was considered since the wing structure was not sufficiently changed to affect its static aeroelastic qualities. The aircraft was found to be free from flutter in all of the normal modes explored in the ground shake test. The analysis demonstrated freedom from flutter up to 214 miles per hour.

Kroeger, R. A.↗

NASA NTRS1978

Estimate of Orbiter static aeroelasticity properties via FLEXSTAB

The theory underlying the use of rigid-model experimental data in FLEXSTAB aeroelasticity calculations is summarized. A description is given of the aerodynamic and structural models used in the calculation of Space Shuttle Orbiter aeroelasticity properties during the re-entry phase. Experience gained with the use of pressure, nonlinear force and moment, and area-ratio correction methods in the Orbiter application is described and typical program output data are included. The inability of the program to correctly estimate differential control surface pressures and to accept external corrections for these terms is shown to be a major limitation in the Orbiter application.

Cavin, R. K., III↗

NASA NTRS1978

On the optimization of discrete structures with aeroelastic constraints

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Mcintosh, S. C., Jr.↗

NASA NTRS1979

Formulation of the aeroelastic stability and response problem of coupled rotor/support systems

The consistent formulation of the governing nonlinear equations of motion for a coupled rotor/support system is presented. Rotor/support coupling is clearly documented by enforcing dynamic equilibrium between the rotor and the moving flexible support. The nonlinear periodic coefficient equations of motion are applicable to both coupled rotor/fuselage aeroelastic problems of helicopters in hover or forward flight and coupled rotor/tower dynamics of a large horizontal axis wind turbine (HAWT). Finally, the equations of motion are used to study the influence of flexible supports and nonlinear terms on rotor aeroelastic stability and response of a large two-bladed HAWT.

Warmbrodt, W.↗

NASA NTRS1978

Some observations on four current subjects related to aeroelastic stability

After introductory comments on the literature and the purposes of this paper, a table is presented summarizing the author's views on some currently solved vs partially unsolved problems related to aeroelastic stability. The term 'solved' is used in the practical sense that engineers are able to cope confidently with that problem during the process of structural design. Selected entries in the table are reviewed, partially to motivate the topics in the rest of the paper. The 'four current subjects' are chosen both for timeliness and because they are among the ongoing interests of the Stanford group. The first involves the prediction of linearized unsteady aerodynamic loads due to arbitrary motions of streamlined shapes. Some contributions by Edwards are refined, which were motivated by the requirements of active control system design. The second subject is nonlinear unsteady aerodynamics for the transonic regime. After describing a few useful developments from locally-linear theory and computational fluid dynamics, there is suggested an empirical procedure for interim-analysis purposes. The third and fourth subjects concern recent discoveries regarding the aeroelastic stability of large-aspect-ratio wings and wind turbines. The former work is mainly that of Petre and Boyd. The latter includes some of the author's own preliminary discoveries about the performance and dynamics of vertical-axis machines.

Ashley, H.↗

NASA NTRS1979

Study of the feasibility aspects of flight testing an aeroelastically tailored forward swept research wing on a BQM-34F drone vehicle

The aspects of flight testing an aeroelastically tailored forward swept research wing on a BQM-34F drone vehicle are examined. The geometry of a forward swept wing, which is incorporated into the BQM-34F to maintain satisfactory flight performance, stability, and control is defined. A preliminary design of the aeroelastically tailored forward swept wing is presented.

Mourey, D. J.↗

NASA NTRS1979

Aeroelastic equations of motion of a Darrieus vertical-axis wind-turbine blade

The second-degree nonlinear aeroelastic equations of motion for a slender, flexible, nonuniform, Darrieus vertical-axis wind turbine blade which is undergoing combined flatwise bending, edgewise bending, torsion, and extension are developed using Hamilton's principle. The blade aerodynamic loading is obtained from strip theory based on a quasi-steady approximation of two-dimensional incompressible unsteady airfoil theory. The derivation of the equations has its basis in the geometric nonlinear theory of elasticity and the resulting equations are consistent with the small deformation approximation in which the elongations and shears are negligible compared to unity. These equations are suitable for studying vibrations, static and dynamic aeroelastic instabilities, and dynamic response. Several possible methods of solution of the equations, which have periodic coefficients, are discussed.

Kaza, K. R. V.↗

NASA NTRS1981

Application of constrained optimization to active control of aeroelastic response

Active control of aeroelastic response is a complex in which the designer usually tries to satisfy many criteria which are often conflicting. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear-Quadratic-Gaussian (LQG) method are of the same high order as the aeroelastic plant. To overcome this disadvantage of the LQG mode, an approach developed for designing low order optimal control laws which uses a nonlinear programming algorithm to search for the values of the control law variables that minimize a composite performance index, was extended to the constrained optimization problem. The method involves searching for the values of the control law variables that minimize a basic performance index while satisfying several inequality constraints that describe the design criteria. The method is applied to gust load alleviation of a drone aircraft.

Newsom, J. R.↗

NASA NTRS1981

A hybrid state vector approach to aeroelastic analysis with application to composite lifting surfaces

A computational technique has been developed for performing preliminary design aeroelastic analyses of large aspect ratio lifting surfaces. This technique, applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. An integrating matrix is employed to solve these equations for divergence and flutter eigenvalues and steady aeroelastic deformation. Results are presented for simple examples which verify the technique and demonstrate how it can be applied to analyze lifting surfaces, including those constructed from composite materials.

Lehman, L. L.↗

NASA NTRS1980

Rotor blade aeroelastic stability and response in forward flight

The aeroelastic stability and response problem of the coupled flap-lag-torsional dynamics of a hingeless rotor blade in forward flight is treated in a comprehensive manner. The spatial dependence of the partial differential, nonlinear, equations of motion is discretized using a multimodal Galerkin method. The aeroelastic problem is coupled with the trim state of the helicopter obtained from improved, representative, trim procedures. The nonlinear time dependent equilibrium position, or response, about which the equations are linearized is obtained by solving a sequence of linear periodic response problems, using quasi-linearization. Numerous results illustrating blade behavior in forward flight are presented.

Friedmann, P. P.↗

NASA NTRS1982

Application of a transonic potential flow code to the static aeroelastic analysis of three-dimensional wings

Since the aerodynamic theory is nonlinear, the method requires the coupling of two iterative processes - an aerodynamic analysis and a structural analysis. A full potential analysis code, FLO22, is combined with a linear structural analysis to yield aerodynamic load distributions on and deflections of elastic wings. This method was used to analyze an aeroelastically-scaled wind tunnel model of a proposed executive-jet transport wing and an aeroelastic research wing. The results are compared with the corresponding rigid-wing analyses, and some effects of elasticity on the aerodynamic loading are noted.

Whitlow, W., Jr.↗

NASA NTRS1982

Application of a transonic potential flow code to the static aeroelastic analysis of three-dimensional wings

A method for including elastic effects in steady, transonic wing analysis is presented. Since the aerodynamic theory is nonlinear, the method requires the coupling of two iterative processes - an aerodynamic analysis and a structural analysis. A full potential analysis code, FL022, is combined with a linear structural analysis to yield aerodynamic load distributions on and deflections of elastic wings. This method was used to analyze an aeroelastically-scaled wind tunnel model of a proposed executive-jet transport wing and an aeroelastic research wing. The results are compared with the corresponding rigid-wing analyses, and some effects of elasticity on the aerodynamic loading are noted.

Whitlow, W., Jr.↗

NASA NTRS1983

Aeroelastic tailoring of rotor blades for vibration reduction in forward flight

Modern structural optimization techniques are applied to vibration reduction of helicopter rotor blades in forward flight. The objective function minimized consists of the oscillatory vertical hub shears or the hub rolling moments at one particular advance ratio. The behavior constraints are the frequency placements of the blade and the requirement that aeroelastic stability margins, in hover, remain unaffected by the optimization process. The aeroelastic stability and response analysis is based on a fully coupled flap-lag-torsional analysis of the blade. The vertical hub shears and rolling moments used as the objective function are obtained by appropriate integration of the loads acting along the span of the blade combined with a transformation to a hub fixed coordinate system, and a summation over the total number of blades. Numerical results for both a stiff-in-plane and a soft-in-plane configuration are presented, indicating that structural optimization yields the highest benefits when applied to soft-in-plane blade configuration. The results indicate substantial (15-40 percent) reduction in vibration levels, as well as a blade which is 20 percent lighter than the initial design.

Friedmann, P. P.↗

NASA NTRS1983

The design, testing and analysis of aeroelastically tailored transonic flutter model wings

An investigation of both the static aeroelastic and flutter characteristics of an aft swept wing, aeroelastically tailored to washout in one design and to washin in another, has been performed using two one-fourth-scale cantilever models representing the two designs. The models have been designed using an MSC/NASTRAN finite element model to preserve the full-scale airplane washout and washin characteristics. Test results show that the effect of the skin-to-core adhesive on model stiffness must be considered in the design cycle. Flutter analyses correlate fairly well with test results. Consideration is also given to F-16 metal and washout wing flutter speeds and mass ratio effects.

Murphy, A. C.↗

NASA NTRS1983

Aeroelastic analysis for propellers - mathematical formulations and program user's manual

Mathematical development is presented for a specialized propeller dedicated version of the G400 rotor aeroelastic analysis. The G400PROP analysis simulates aeroelastic characteristics particular to propellers such as structural sweep, aerodynamic sweep and high subsonic unsteady airloads (both stalled and unstalled). Formulations are presented for these expanded propeller related methodologies. Results of limited application of the analysis to realistic blade configurations and operating conditions which include stable and unstable stall flutter test conditions are given. Sections included for enhanced program user efficiency and expanded utilization include descriptions of: (1) the structuring of the G400PROP FORTRAN coding; (2) the required input data; and (3) the output results. General information to facilitate operation and improve efficiency is also provided.

Bielawa, R. L.↗

NASA NTRS1984

Unsteady transonic aerodynamic and aeroelastic calculations about airfoils and wings

The development and application of transonic small disturbance codes for computing two dimensional flows, using the code ATRAN2, and for computing three dimensional flows, using the code ATRAN3S, are described. Calculated and experimental results are compared for unsteady flows about airfoils and wings, including several of the cases from the AGARD Standard Aeroelastic Configurations. In two dimensions, the results include AGARD priority cases for the NACA 64A006, NACA 64A010, NACA 0012, and MBB-A3 airfoils. In three dimensions, the results include flows about the F-5 wing, a typical wing, and the AGARD rectangular wings. Viscous corrections are included in some calculations, including those for the AGARD rectangular wing. For several cases, the aerodynamic and aeroelastic calculations are compared with experimental results.

Goorjian, P. M.↗

NASA NTRS1982

On-line methods for rotorcraft aeroelastic mode identification

The requirements for the on-line identification of rotorcraft aeroelastic blade modes from random response test data are presented. A recursive maximum likelihood (RML) technique is used in conjunction with a bandpass filter to identify isolated blade mode damping and frequency. The RML technique is demonstrated to have excellent convergence characteristics in random measurement noise and random process noise excitation. The RML identification technique uses an ARMA representation for the aeroelastic stochastic system and requires virtually no user interaction while providing accurate confidence bands on the parameter estimates. Comparisons are made with an off-line Newton type maximum likelihood algorithm which uses a state variable model representation. Results are presented from simulation random response data which quantify the identifed parameter convergence behavior for various levels of random excitation which is typical of wind tunnel turbulence levels. The RML technique is applied to hingless rotor test data from the NASA Langley Research Center Helicopter Hover Facility.

Molusis, J. A.↗

NASA NTRS1985

Unsteady transonic flow calculations for two-dimensional canard-wing configurations with aeroelastic applications

Unsteady transonic flow calculations for aerodynamically interfering airfoil configurations are performed as a first step toward solving the three dimensional canard wing interaction problem. These calculations are performed by extending the XTRAN2L two dimensional unsteady transonic small disturbance code to include an additional airfoil. Unsteady transonic forces due to plunge and pitch motions of a two dimensional canard and wing are presented. Results for a variety of canard wing separation distances reveal the effects of aerodynamic interference on unsteady transonic airloads. Aeroelastic analyses employing these unsteady airloads demonstrate the effects of aerodynamic interference on aeroelastic stability and flutter. For the configurations studied, increases in wing flutter speed result with the inclusion of the aerodynamically interfering canard.

Batina, J. T.↗