Flutter Dynamic Pressure Research Articles

Open- and closed-loop results of a strain-actuated active aeroelastic wing

Open- and closed-loop tests for a strain-actuated active aeroelastic wing are summarized. Linear quadratic Gaussian (LQG) control laws as well as robust control laws are designed using sensitivity weighted LQG, classical rationalization, and multiple models. Significant vibration suppression and load alleviation are demonstrated, reducing the power spectral density of the first mode's response by an order of magnitude. The flutter dynamic pressure is increased by 12%. The three major performance limitations are the saturation limit of the piezoelectrics, the choice of performance metric or output sensor, and the changes in the dynamic response of the test article. T

Flutter margin augmentation synthesis using normalized coprime factors approach

This research is concerned with the design of a flutter margin augmentation system at a supercritical flutter condition subject to control capacity constraints. The control law is synthesized using the //oo loop-shaping method at the normalized coprime factors framework, and order reduction processes are applied to both the nominal plant and the synthesized controller. The effects of output weighting on the control capacity and the influence of the controller suboptimality over its reduction process are further investigated. Robust stability analyses dealing with unstructured uncertainties and sensitivity studies by variation of the fundamental flutter parameters are presented. In transonic wind-tunnel tests, the resulting fourth-order digital controller extends the closed-loop flutter dynamic pressure of an aeroservoelastic wing model by 11.4% over its open-loop value, despite discrepancies in the analytically predicted flutter parameters. Nomenclature B = process noise distribution matrix g = gravity acceleration K®S(s) = gain from output disturbance to controller output K®SG(s) = gain from input disturbance to controller output S(s) = gain from output disturbance to plant output SG(s) = gain from input disturbance to plant output W = intensity matrix r] = zero-mean Gaussian white-noise process

Flutter suppression control law design and testing for the active flexible wing

Design of a control law for simultaneously suppressing the symmetric and antisymmetric flutter modes of a sting-mounted, fixed-in-roll aeroelastic wind-tunnel model is described. The flutter suppression control law was designed using linear quadratic Gaussian theory, and involved control law order reduction, a gain root-locus study, and use of previous experimental results. A 23% increase in the open-loop flutter dynamic pressure was demonstrated during the wind-tunnel test. Rapid roll maneuvers at 11% above the symmetric flutter boundary were also performed when the model was in a free-to-roll configuration.

Flutter suppression for the active flexible wing - A classical design

The synthesis and experimental validation of a control law for an active flutter suppression system for the active flexible wing wind-tunnel model is presented. The design was accomplished with traditional root locus methods making extensive use of interactive computer graphics tools and simulation-based analysis. The design approach relied on a fundamental understanding of the flutter mechanism to formulate a very simple control law structure resulting in a filter with a inverted notch characteristic. This unusual filter characteristic was required to compensate for adverse zero locations in the frequency range near flutter. Wind-tunnel tests of the flutter suppression controller demonstrated simultaneous suppression of two flutter modes, significantly increasing the flutter dynamic pressure. The flutter suppression controller was also successfully operated in combination with a rolling maneuver controller to perform flutter suppression during rapid rolling maneuvers.

Rolling maneuver load alleviation using active controls

Rolling maneuver load alleviation using active controls

Aeroelastic effects of spoiler surfaces on a low-aspect-ratio rectangular wing

An experimental research study to determine the effectiveness of spoiler surfaces in suppressing flutter onset for a low-aspect-ratio, rectangular wing has been conducted in the Langley Transonic Dynamics Tunnel (TDT). The wing model used in this flutter test consisted of a rigid wing mounted to the wind-tunnel wall by a flexible, rectangular beam. The flexible beam was connected to the wing root and cantilever mounted to the wind-tunnel wall. The wing had a 1.5 aspect ratio based on wing semispan and a NACA 64AGIO airfoil shape. The spoiler surfaces consisted of thin, rectangular aluminum plates that were vertically mounted to the wing surface. The spoiler surface geometry and location on the wing surface were varied to determine the effects of these parameters on the classical flutter of the wing model. Subsonically, the experiment showed that spoiler surfaces increased the flutter dynamic pressure with each successive increase in spoiler height or width. This subsonic increase in flutter dynamic pressure was approximately 15% for the maximum height spoiler configuration and for the maximum width spoiler configuration. At transonic Mach numbers, the flutter dynamic pressure conditions were increased even more substantially than at subsonic Mach numbers for some of the smaller spoiler surfaces. But for larger spoiler sizes (in terms of either height or width) the spoilers forced a torsional instability in the transonic regime that was highly Mach number dependent. This detrimental torsional instability was found at dynamic pressures well below the expected flutter conditions. Variations in the span wise location of the spoiler surfaces on the wing showed little effect on flutter. Flutter analysis was conducted for the basic configuration (clean wing with all spoiler surface mass properties included). The analysis correlated well with the clean wing experimental flutter results.

Multidisciplinary optimization of aeroservoelastic systems using reduced-size models

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

Parametric aeroelastic stability analysis of a generic X-wing aircraft

This paper discusses the dynamic aeroelastic stability of a generic X-wing aircraft configuration. The analysis model includes rigid-body degrees of freedom and unsteady aerodynamic forces generated using the doublet lattice method. Design parameters are varied to evaluate the trends in dynamic aeroelastic stability. X-wing rotor blade sweep angle, ratio of blade mass to total vehicle mass, blade structural stiffness cross coupling, and vehicle center of gravity location were parameters considered. The typical instability encountered is body-freedom flutter involving a low-frequency interaction of the first elastic mode and the aircraft short period mode. In most parametric cases, those cases having the least static longitudinal stability demonstrated the highest flutter dynamic pressures. As mass ratio was increased, the flutter boundary decreased. The decrease was emphasized as center of gravity location was moved forward. As sweep angle varied, it was observed that the resulting increase in forward-swept blade bending amplitude relative to aft blade bending amplitude in the first elastic mode had a stabilizing effect on the flutter. b [B,] [C' [C] El [F] GJ [7] ^ [K] [Kf] L Lb [M'] mb nif mr [M] q

Sensitivity derivatives of flutter characteristics and stability margins for aeroservoelastic design

Analytical derivatives of flutter dynamic pressure, flutter frequency, gain margins, and phase margins with respect to various aeroservoelastic design variables are developed. The formulation is based on a first-order time-domain aeroservoelastic mathematical model. The structure is represented in the model by vibration modes, the unsteady aerodymanics by minimum-state rational approximation functions, and the control system is coupled with the aeroelastic system through motion sensors and control surfaces. The sensitivity derivatives are expressed as exact functions of the stability boundary eigenvectors and of the real-valued system matrix derivatives with respect to arbitrary design variables. These expressions may be applied to any aeroservoelastic design variable with respect to which the system matrix derivative is available. System matrix derivatives with respect to structural stiffness and mass parameters, control gains, actuator parameters, and sensor locations are presented. The new sensitivity derivatives facilitate efficient gradient-based aeroservoelastic algorithms, which directly address flutter and stability margin requirements. A numerical example utilizing the mathematical model of the Active Flexible Wing wind-tunnel model is given. A practical control design problem with roll maneuver constraints is used to demonstrate the accuracy and usage of the derivatives.

Design of a flutter mode controller using positive real feedback

The use of positive real feedback for the design of a flutter mode control system is examined. Results indicate that this technique is a meaningful synthesis procedure for the design of low-order controllers. The synthesis is achieved through the design of a positive real observer using a low-order approximation to the governing system equations. Results obtained for a realistic aeroelastic model show that flutter dynamic pressure can be increased by more than 50%. The effect of unmpdeled phase shift caused by aerodynamic and actuation lags can be avoided in the positive real design by suitable choice of control bandwidth. This technique thus appears as a viable design technique for flutter and aeroelastic modal control.

Nonlinear panel flutter using high-order triangular finite elements

A 54 degree-of-freedom, high-order triangular plate finite element extended for geometrically nonlinear static and dynamic analysis is used to formulate and analyze the supersonic nonlinear panel flutter problems. The finite element formulation is based on Kirchhoffs theory of thin plates. The quasisteady aerodynamic theory is used. Numerical solution procedures are presented. The limit cycle oscillation analyses are performed for twodimensional and square panels with all edges simply supported and clamped, respectively. The effects of in-plane compressive force, mass ratio, and in-plane edge stress free condition are considered. Stress distributions for the limit cycle oscillation of a two-dimensional panel are plotted. For the case of panels under static pressure differential, the results for the steady mean amplitude and flutter dynamic pressure are obtained for the twodimensional and square panels, respectively. The effect of biaxial in-plane compressive stress for a simply supported square panel is studied and boundaries among the flat and stable region, dynamically stable buckled region, and the limit cycle oscillation region are found. Alternative analytical and numerical solutions are available for most of the examples for comparison and all are in excellent agreement.

F-16 Flutter Suppression System Investigation Feasibility Study and Wind Tunnel Tests

A study was conducted to determine the feasibility of employing active controls on the F-16 to suppress wing- store flutter for several external store configurations. It was determined that the existing flaperons, with modifications to the integrated servoactuators, were effective in suppressing flutter. The F-16 flutter model was tested with active flaperons. Open-loop frequency response functions (FRF's) were successfully measured in the wind tunnel environment both with the feedback loop physically opened and with the loop closed. These measurements provided guidance in the selection of sensor locations and feedback control laws to suppress flutter. Control law variations were made to obtain the desired FRF characteristics. A 100% increase in dynamic pressure above the flutter dynamic pressure was demonstrated. IGHTER aircraft are required to carry a very large number of external store configurations. The probability is high that at least a small subset of these configurations will flutter within the desired operational envelope of the airplane. This probability is further increased as new stores are added to the operational airplane inventory. When wing-store flutter problems occur, the solution requires a modification of the airplane (usually a change in stiffness and weight) and/or a speed restriction which reduces the operational envelope of the airplane. Flutter suppression with active controls is another solution which has been investigated in recent years. Several approaches have been taken to design these sys- tems.1-3 One of the more promising approaches to the design of calibrated active control systems is the frequency response method. This approach is attractive because of the state of development of methods for computing oscillatory aerodynamic pressure distributions, because frequency response functions (FRF's) are experimentally measurable, and because the military specification for the stability of aeroservoelastic systems is based on the Nyquist criteria. This method was applied in a flutter suppression system (FSS) feasibility study4 for the F-4. The results of this study indicate that the milder flutter modes and the lower flutter frequencies associated with wing-store configurations could be relatively easily suppressed with active controls. The initial design approach for the active control system for the YF-17 semispan flutter model was the root locus method.5 However, a modified Nyquist approach was subsequently used.6 The Nyquist stability criteria has been applied extensively by Turner.7 The Nyquist criteria was employed as the principal design tool in the F-16 FSS investigations. For the system with negative feedback shown in Fig. 1, the transfer function for the closed loop system is

Recent Development of the YF-17 Active Flutter Suppression System

Active wing/store flutter suppression systems were demonstrated in 1977 in a series of wind tunnel tests on a YF-17 scale model. In order to substantially improve the suppression system performance, new control laws were developed based on multiple feedback loops, multiple control surfaces, or both. For test safety, a flutter sensing unit and a new store, functioning as a flutter stopper, were designed and fabricated. Test monitoring programs were organized on a Hewlett-Packard 5451C Fourier Analyzer that permitted a real time assessment of the control law effectiveness. One of the monitoring programs generated the aircraft open loop transfer function and Nyquist plots in the supercritical region while the flutter suppression loop was closed. In the tests performed in late 1979, the new control laws were applied to suppress a severe flutter condition to 70% above the uncontrolled flutter dynamic pressure. Postanalysis of the test data indicated the potential to increase the dynamic pressure to an even higher level.

Active External Store Flutter Suppression in the YF-17 Flutter Model

A single activated trailing-edge (T.E.) control system (spanning 7% of each wing) is applied to the YF-17 flutter model with the object of suppressing the external store flutter of three different store configurations. The control law is derived by the use of the aerodynamic energy concept and its gains are maintained constant for all three configurations. The results obtained show that the activated T.E. control system leads to very significant increases in the flutter dynamic pressures Q(DF) of all three configurations; these increases range between 160-240% increase in Q(DF). These increases in Q(DF) are maintained over a very wide range of flight altitudes and flight velocities.

Control Law Synthesis for Active Flutter Suppression Using Optimal Control Theory

This paper describes a study investigating the use of optimal control theory for the synthesis of an active flutter-suppression control law. For an example design application, a high-aspect-ratio cantilever wind-tunnel wing model is considered. The structural dynamics are represented by analytically computed natural frequencies and mode shapes. The three-dimensional unsteady aerodynamic forces for oscillatory motion are computed employing the doublet-lattice technique. With the aid of finite-order approximating functions for representing the aerodynamic forces in the time domain, the equations are written in the standard state vector form. Linear optimal control theory is then applied to find particular sets of gain values which minimize a quadratic cost function of the states and controls. These control laws are shown to increase the flutter dynamic pressure by at least 50% at Mach numbers 0.7 and 0.9. The closed-loop system's control surface activity in a gust environment is also examined.

Comparative Study Between Two Different Active Flutter Suppression Systems

An activated leading-edge (LE)-tailing-edge (TE) control system is applied to a drone aircraft with the objective of enabling the drone to fly subsonically at dynamic pressures which are 44% above the open-loop flutter dynamic pressure. The control synthesis approach is based on the aerodynamic energy concept and it incorporates recent developments in this area. A comparison is made between the performance of the activated LE-TE control system and the performance of a TE control system, analyzed in a previous work. The results obtained indicate that although all the control systems achieve the flutter suppression objectives, the TE control system appears to be somewhat superior to the LE-TE control system, in this specific application. This superiority is manifested through reduced values of control surface activity over a wide range of flight conditions.

Flutter and Buckling of General Laminated Plates

An anisotropic buckling and flutter analysis is developed with allowance for both bending-extensional coupling and bending-twisting coupling within the framework of linear small deflection theory for simply supported general laminated plates. The extended Galerkin method is used to obtain approximate solutions to the coupled governing equations. The effects of various anisotropic stiffness parameters on the static and dynamic stability of laminated plates are evaluated, with particular emphasis on assessing the range of applicability of classical orthotropic plate theory. It is shown that bending-extensional coupling and bending-twisting stiffness terms have a destabilizing effect on buckling and flutter, the effect being more pronounced for a small number of layers. For symmetric plates, the number of layers required for orthotropic plate theory to be applicable is generally less for the buckling problem than for flutter. For square plates, aligning the fibers with the direction of airflow over the plate surface results in the highest flutter dynamic pressure.

Boundary-layer effect in panel flutter

The present note shows that if the supersonic Mach number is not too large, an analytical expression can be obtained for the generalized aerodynamic force relating the pressure fluctuation at the surface of a flexible plate to the plate displacement in the presence of an adjacent boundary layer. The low supersonic Mach numbers are the ones of maximum interest since it is in this Mach number region that the boundary layer has the most influence. In this respect, Dowell (1971) has already shown that the presence of a boundary layer causes about a 300% increase in flutter dynamic pressure at a Mach number of about 1.2, while it causes only about a 20% increase at a Mach number of 2.

SKIN-FRICTION-WORK RECOVERY BY AERODYNAMIC HEATING OF SKIN COOLANTS

These primitive panel modes are not orthogonal; however, for the present purposes we may reasonably neglect the structural coupling and also the coupling between modes due to the cavity. Thus we shall treat each panel mode individually. Eqs. (7), (8), and (9) have been solved by the Galerkin method. A comparison of the present theoretical results with previously obtained experimental results is presented in Figs. 2 and 3. In obtaining the theoretical curves the experimental values of the in vacuo frequencies were used. In Fig. 2 a plot of frequency vs cavity depth at standard atmospheric conditions is shown. Since considerably lower air densities are encountered in the wind tunnel, the variation of frequency with cavity densitv has been determined as well (see Fig. 3). As may be seen, the agreement between theory and experiment is good except at the smaller cavity depths and densities. In particular, the change in the mode of minimum frequency predicted by theory is confirmed by the experimental data, with reasonable agreement on the cavity depth for which it occurs. One may hypothesize that an inclusion of nonlinear and/or viscous effects would bring the theory into better agreement with the experimental results at the smaller cavity depths and densities. A theoretical calculation of the flutter dynamic pressure has been made for the tested panel with a cavity depth of three inches. The result indicates a decrease in flutter dynamic pressure of the order of 20 percent at Mach 2 with zero pressure differential across the panel. In many practical cases only the fundamental mode will be modified by the aerodynamic-spring effect and the virtualmass effect may be neglected. For this case a useful approximate formula may be written for the frequency of the fundamental mode—viz.,