Showing papers on "Aeroelasticity published in 1977"

Unsteady aerodynamic modeling for arbitrary motions

Abstract: A study is presented on the unsteady aerodynamic loads due to arbitrary motions of a thin wing and their adaptation for the calculation of response and true stability of aeroelastic modes. In an Appendix, the use of Laplace transform techniques and the generalized Theodorsen function for two-dimensional incompressible flow is reviewed. New applications of the same approach are shown also to yield airloads valid for quite general small motions. Numerical results are given for the two-dimensional supersonic case. Previously proposed approximate methods, starting from simple harmonic unsteady theory, are evaluated by comparison with exact results obtained by the present approach. The Laplace inversion integral is employed to separate the loads into 'rational' and 'nonrational' parts, of which only the former are involved in aeroelastic stability of the wing. Among other suggestions for further work, it is explained how existing aerodynamic computer programs may be adapted in a fairly straightforward fashion to deal with arbitrary transients.

Finite state modeling of aeroelastic systems

Abstract: A general theory of finite state modeling of aerodynamic loads on thin airfoils and lifting surfaces performing completely arbitrary, small, time-dependent motions in an airstream is developed and presented. The nature of the behavior of the unsteady airloads in the frequency domain is explained, using as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. The modeling technique is applied to several two dimensional and three dimensional airfoils. Circular, elliptic, rectangular and tapered planforms are considered as examples. Identical functions are also obtained for control surfaces for two and three dimensional airfoils.

Unsteady aerodynamic modeling for arbitrary motions

Abstract: Results indicating that unsteady aerodynamic loads derived under the assumption of simple harmonic motions executed by airfoil or wing can be extended to arbitrary motions are summarized. The generalized Theodorsen (1953) function referable to loads due to simple harmonic oscillations of a wing section in incompressible flow, the Laplace inversion integral for unsteady aerodynamic loads, calculations of root loci of aeroelastic loads, and analysis of generalized compressible transient airloads are discussed.

Unsteady aerodynamic modeling and active aeroelastic control

Abstract: Unsteady aerodynamic modeling techniques are developed and applied to the study of active control of elastic vehicles. The problem of active control of a supercritical flutter mode poses a definite design goal stability, and is treated in detail. The transfer functions relating the arbitrary airfoil motions to the airloads are derived from the Laplace transforms of the linearized airload expressions for incompressible two dimensional flow. The transfer function relating the motions to the circulatory part of these loads is recognized as the Theodorsen function extended to complex values of reduced frequency, and is termed the generalized Theodorsen function. Inversion of the Laplace transforms yields exact transient airloads and airfoil motions. Exact root loci of aeroelastic modes are calculated, providing quantitative information regarding subcritical and supercritical flutter conditions.

Recent developments in rotary-wing aeroelasticity

Abstract: The purpose of this review is to present the research done in rotary-wing aeroelasticity during the past eight years in a unified manner. The following topics are reviewed with considerable detail: (1) recent development in the aeroelastic modeling of the coupled flap-lag-torsional problem in hover (2) effect of unsteady aerodynamics on the coupled flap-lag-torsional aeroelastic problem in hover (3) the coupled flap-lag and the coupled flap-lag-torsional problem in forward flight (4) complete rotor and coupled rotor fuselage aeroelastic problems including both hingeless and teetering rotors.

Motion of Suspension Bridge Subject to Wind Loads

Abstract: Vertical and torsional motions of a suspension bridge due to wind loading are studied. Both, self-excited, due to bridge motion, and buffeting, independent of bridge motion, wind loads are included. The self-excited aerodynamic forces are modeled using aerodynamic coefficient or Duhamel integral formulations. For this purpose, experimental information on section models from wind tunnel testing is utilized. The buffeting random loads are determined from specified spectral densities or horizontal and vertical turbulent wind velocity fluctuations. Numerical results are obtained using frequency and time domain formulations. Dynamic bridge stability is also investigated.

Effect of Modified Aerodynamic Strip Theories on Rotor Blade Aeroelastic Stability

Abstract: Various existing unsteady aerodynamic strip theories which have been developed in the past for both fixed and rotary wing aeroelastic analyses are modified in the paper so as to make them applicable to the coupled flap-lag-torsional aeroelastic problem of a rotor blade in hover. These corrections are primarily due to constant angle of attack, constant inflow and variable free stream velocity due to lead-lag motion. Next, the modified strip theories are incorporated in a coupled flap-lag-torsional aeroelastic analysis of the rotor blade in hover and the sensitivity of the aeroelastic stability boundaries to the aerodynamic assumptions is examined.

Influence of Modeling and Blade Parameters on the Aeroelastic Stability of a Cantilevered Rotor

Abstract: A set of equations describing the coupled flap-lag-torsional dynamics of a cantilevered rotor blade in hover is presented. This set of equations is used to evaluate the influence of structural damping, preconing, and offsets on the linearized aeroelastic stability of some representative blade configurations. The sensitivity of the stability boundaries to the assumptions of approximate linear vs exact nonlinear static blade equilibrium position is considered. Finally, results with the distributed torsional representation of blade properties are compared with those obtained when the root torsional model is used.

Measurement of model aeroelastic deformations in the wind tunnel at transonic speeds using stereophotogrammetry

Abstract: A stereophotographic method of determining the aeroelastic deformations of an airplane model under aerodynamic load in the wind tunnel was evaluated. Wind tunnel tests were conducted in the Langley 8 foot transonic pressure tunnel on the wing of a 0.0625 scale model of the TF-8A supercritical wing research airplane to obtain simultaneously the aerodynamic forces and moments, pressure distributions, and stereophotographs. Tests were conducted at Mach numbers of 0.80, 0.95, and 1.20, and at free stream dynamic pressures of 20,349 Pa and 40,698 Pa. Accuracy of the stereophotographic technique in determining wing deflections was within 0.013 cm under static conditions. This value translates to an error in wing twist of 0.10 deg inboard and increases to 0.20 deg outboard. When the model was under aerodynamic load in the wind tunnel, the accuracy of the stereophotographic technique of determining wind deflections increased to 0.052 cm when compared with static wing loadings because of the dynamic motion of the model in the tunnel.

Efficient numerical treatment of periodic systems with application to stability problems. [in linear systems and structural dynamics

Abstract: Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet–Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.

Evaluation of structural design concepts for an arrow-wing supersonic cruise aircraft

Abstract: An analytical study was performed to determine the best structural approach for design of primary wing and fuselage structure of a Mach 2.7 arrow wing supersonic cruise aircraft. Concepts were evaluated considering near term start of design. Emphasis was placed on the complex interactions between thermal stress, static aeroelasticity, flutter, fatigue and fail safe design, static and dynamic loads, and the effects of variations in structural arrangements, concepts and materials on these interactions. Results indicate that a hybrid wing structure incorporating low profile convex beaded and honeycomb sandwich surface panels of titanium alloy 6Al-4V were the most efficient. The substructure includes titanium alloy spar caps reinforced with boron polyimide composites. The fuselage shell consists of hat stiffened skin and frame construction of titanium alloy 6Al-4V. A summary of the study effort is presented, and a discussion of the overall logic, design philosophy and interaction between the analytical methods for supersonic cruise aircraft design are included.

Subsonic Transient Lifting Surface Aerodynamics

Abstract: A method is presented for numerical evaluation of subsonic transient lifting surface aerodynamics. Existing subsonic oscillatory aerodynamic procedures are modified to evaluate generalized aerodynamic forces as two matrices: aerodynamic stiffness and damping. Transfer functions are evaluated numerically which describe the complex variation with reduced frequency of each matrix element. The results are used to formulate the aeroelastic equations of motion in the Laplace operator and real time domains. The Laplace operator formulation is applied to transient flutter solutions, and the results are compared to conventional solutions. The time formulation is applied to several time history dynamic response configurations.

Aeroelastic Characteristics of Composite Bearingless Rotor Blades

Abstract: Owing to the inherent unique structural features of composite bearingless rotors, various assumptions upon which conventional rotor aeroelastic analyses are formulated, are violated. Three such features identified are highly nonlinear and time-varying structural twist, structural redundancy in bending and torsion, and for certain configurations a strongly coupled low frequency bending-torsion mode. An examination of these aeroelastic considerations and appropriate formulations required for accurate analyses of such rotor systems is presented. Also presented are test results from a dynamically scaled model rotor and complementary analytic results obtained with the appropriately reformulated aeroelastic analysis.

Effects of Flow Separation on Shuttle Longitudinal Dynamics and Aeroelastic Stability

Abstract: The longitudinal dynamic and aeroelastic stability characteristics of various shuttle configurations have been investigated at transonic speeds. Wing flow separation dominates the orbiter dynamic stability in a manner that indicates a potential aeroelastic problem for the first torsional mode of the orbiter wing. Throughout the transonic speed range, flow separations of various types are shown to dominate both dynamic and aeroelastic stability of the launch configuration, causing limit cycle oscillations of certain symmetric elastic modes. The limit cycle oscillations threaten the structural integrity in two ways: 1) by outright overstressing of the structure due to large modal deflection, and 2) by fatigue due to the continued flexing of the structure. Fatigue is a more significant consideration for the reusable (100 flights) shuttle than it has been for previous space boosters, especially in view of the coexisting problem of thermocycling.

Effect of chordwise forces and deformations and deformations due to steady lift on wing flutter

Abstract: This investigation explores the effects of chordwise forces and deformations and steady-state deformation due to lift on the static and dynamic aeroelastic stability of a uniform cantilever wing. Results of this analysis are believed to have practical applications for high-performance sailplanes and certain RPV's. The airfoil cross section is assumed to be symmetric and camber bending is neglected. Motions in vertical bending, fore-and-aft bending, and torsion are considered. A differential equation model is developed, which included the nonlinear elastic bending-torsion coupling that accompanies even moderate deflections. A linearized expansion in small time-dependent deflections is made about a steady flight condition. The stability determinant of the linearized system then contains coefficients that depend on steady displacements. Loads derived from two-dimensional incompressible aerodynamic theory are used to obtain the majority of the results, but cases using three-dimensional subsonic compressible theory are also studied. The stability analysis is carried out in terms of the dynamically uncoupled natural modes of vibration of the uniform cantilever.

An Algorithm for Autonomous Non-linear Dynamical Equations

Abstract: The method of Beecham and Titchener is extended to systems with n degrees of freedom and is shown to be a combination of the averaging principle and the method of variation of parameters. In this extended form, the method provides a powerful solution algorithm for non-linear problems such as those which arise in aircraft structural dynamics and aeroelasticity. The method is exemplified in application to a two-degree-of-freedom damped non-linear oscillator and to a binary (flexure-aileron) non-linear flutter system. The method is finally extended to non-linear differential equations in first-order form such as those which arise commonly in flight mechanics.

F-16 flutter model studies with external wing stores

Abstract: Results from transonic flutter model studies are presented. The flutter model was constructed to support the flutter prevention and clearance program from preliminary design through flight flutter tests. The model tests were conducted in the Langley transonic dynamics tunnel. The large full span free-flying model was shown to be an effective tool in defining airplane flutter characteristics by demonstrating freedom from flutter for most configurations and by defining optimum solutions for a few troublesome configurations.

Aeroelastic analysis for rotorcraft in flight or in a wind tunnel

Abstract: An analytical model is developed for the aeroelastic behavior of a rotorcraft in flight or in a wind tunnel. A unified development is presented for a wide class of rotors, helicopters, and operating conditions. The equations of motion for the rotor are derived using an integral Newtonian method, which gives considerable physical insight into the blade inertial and aerodynamic forces. The rotor model includes coupled flap-lag bending and blade torsion degrees of freedom, and is applicable to articulated, hingeless, gimballed, and teetering rotors with an arbitrary number of blades. The aerodynamic model is valid for both high and low inflow, and for axial and nonaxial flight. The rotor rotational speed dynamics, including engine inertia and damping, and the perturbation inflow dynamics are included. For a rotor on a wind-tunnel support, a normal mode representation of the test module, strut, and balance system is used. The aeroelastic analysis for the rotorcraft in flight is applicable to a general two-rotor aircraft, including single main-rotor and tandem helicopter configurations, and side-by-side or tilting proprotor aircraft configurations.

Computation of unsteady transonic flows by the indicial method

Abstract: The indicial method is investigated for the computation of unsteady transonic force and moment coefficients for use in flutter analyses. This approach has the advantage that solutions for all reduced frequencies for a given mode of motion can be obtained from a single finite-difference flowfield computation. Comparisons of indicial and time-integration computations for oscillating airfoil and flap motions help define limits on the motion amplitude for the applicability of the indicial method to transonic flows. Within these limits, solutions for various motion modes can be superposed to obtain solutions for multiple-degree-of-freedom aeroelastic systems. Also, a simple aeroelastic problem is solved by an alternative approach in which the structural motion and flowfield equations are integrated simultaneously using a time-integration finite-difference procedure.

Prediction of Elastic-Airplane Lateral Dynamics from Rigid-Body Aerodynamics

Abstract: Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at the early stages of preliminary design and development. For these early analyses an approximate, but reasonably accurate, set of equations of motion for elastic airplanes is needed. Such a formulation is developed for the lateral dynamics of elastic airplanes. It makes use of rigid-body aerodynamic stability derivatives and the antisymmetric elastic mode shapes and frequencies in formulating the forces and moments due to elastic motion. Verification of accuracy was made by comparison with B-1 airplane dynamics obtained by other methods. Frequencies and damping ratios of the coupled modes agree acceptably well with four antisymmetric elastic modes included.

Aeroelastic Stability of the 747/0rbiter

Abstract: A quasisteady analysis of the aeroelastic stability of the lateral (antisymmetric) modes of the 747/Orbiter vehicle demonstrates that the interference effect of the Orbiter wake on the 747 tail furnishes an aerodynamic undamping contribution to the low-frequency elastic modes. Likewise, the upstream influence of the 747 tail and aft fuselage on the Orbiter beavertail tail fairing also is undamping. Fortunately, these undamping effects cannot overpower the large damping contribution of the 747 tail, and the yaw modes are damped for the configurations analyzed.

Comparisons of Theoretical and Experimental Pressure Distributions on an Arrow-Wing Configuration at Subsonic, Transonic, and Supersonic Speeds

Abstract: A wind tunnel test of an arrow wing body configuration consisting of flat and twisted wings, as well as a variety of leading- and trailing-edge control surface deflection, has been conducted at Mach numbers from 0.40 to 2.50 to provide an experimental data base for comparison with theoretical methods. Theory-to-experiment comparisons of detailed pressure distributions have been made using current state-of-the-art attached- and separated-flow methods. The purpose of these comparisons was to delineate conditions under which these theories are valid for aeroelastic calculations and to explore the use of empirical methods to correct the theoretical methods where theory is deficient. It was determined that current state-of-the-art attached flow and empirical methods were inadequate to predict aeroelastic loads for this configuration.

Efficient solution of unsteady transonic flows about airfoils

Abstract: An implicit finite difference procedure was developed for the efficient solution of unsteady transonic flow fields. Sample computations illustrate applications of procedures to aerodynamic problems. Solutions are presented that illustrate three types of shock wave motion that can result from airfoil control surface oscillations. The significant effect of wind tunnel wall conditions on these shock wave motions is demonstrated. Solutions are also presented for a simple aeroelastic problem in which the flow field equations and the structural motion equations are integrated simultaneously in time. Both stable and unstable aeroelastic interactions are considered. The procedure is adapted to compute unsteady aerodynamic force coefficients by the indicial method.

High Reynolds Number Research

Abstract: Fundamental aerodynamic questions for which high Reynolds number experimental capability is required are discussed. The operational characteristics and design features of the National Transonic Facility are reviewed.

Load and stability measurements on a soft-inplane rotor system incorporating elastomeric lead-lag dampers

Abstract: An experimental investigation was conducted of the dynamic response and inplane stability associated with a new soft-inplane helicopter rotor. The unique feature of this rotor was the use of an internal elastomeric damper to restrain the blade inplane motion about the lead-lag hinge. The properties of the elastomer were selected to provide both a nominal first inplane frequency ratio of 0.65 and sufficient damping to eliminate the need for additional external damping sources to prevent ground resonance on a typical fuselage structure. For this investigation a 1/5-scale aeroelastic model was used to represent the rotor. The four-blade model had a diameter of 3.05 m (10 ft) and a solidity of 0.103. The first out-of-plane frequency ratio was 1.06. The model was tested in hover and in forward flight up to an advance ratio of 0.45. At each forward speed the rotor lift was varied up to simulated maneuver conditions. The measured rotor loads and response were within acceptable limits, and no adverse response qualities were observed. Moderate out-of-plane hub moments were measured, even for zero lift, to indicate the beneficial control power available for this design. Blade inplane stability testing indicated that the rotor system damping remained at moderate levels throughout the operating envelope.

The Aeroelastic Analysis of a Two-Dimensional Airfoil in Transonic Flow.

Abstract: : A procedure is developed for the aeroelastic analysis of a two-dimensional airfoil in transonic flow. The fluid is assumed to be described by the unsteady low frequency small disturbance transonic potential equation for which a fully time implicit method of integration (LTRAN2) exists. Structural equations of motion for a three degree of freedom NACA 64A010 airfoil are integrated in time simulataneously with the unsteady potential equation using representative values of the structural parameters. The method is shown to be both stable and accurate, and the time response for several choices of initial conditions and reduced freestream density is presented. Oscillations with either increasing or decreasing amplitudes are found to result solely from the choice of initial conditions. (Author)