On the stability of the equilibrium of nonconservative continuous systems with slight damping.
Stability of equilibrium of nonconservative continuous systems with slight damping
VIBRATION DAMPING↗
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Experimental determination of the inertia constants of an airplane or of a missile
The possibility to measure the inertia constants of an airplane or of a missile by a unique experimental set up without having to materialize axes of rotation was investigated. It is sufficient to suspend the structure appropriately, to obtain the six natural modes determined by the suspension and to introduce these results as data into a computer. If the structure is very flexible it is necessary to take into account the first natural modes of deformation. Experiments on rigid and flexible models led to precise results and allow consideration of full scale measurements. The final goal is to provide, by a standard ground vibration test completed by the measured characteristics of the suspension modes, the set of data necessary for flutter calculations and for the determination of all the inertia constants.
Loiseau, H.↗
Quiet High Speed Fan (QHSF) Flutter Calculations Using the TURBO Code
A scale model of the NASA/Honeywell Engines Quiet High Speed Fan (QHSF) encountered flutter wind tunnel testing. This report documents aeroelastic calculations done for the QHSF scale model using the blade vibration capability of the TURBO code. Calculations at design speed were used to quantify the effect of numerical parameters on the aerodynamic damping predictions. This numerical study allowed the selection of appropriate values of these parameters, and also allowed an assessment of the variability in the calculated aerodynamic damping. Calculations were also done at 90 percent of design speed. The predicted trends in aerodynamic damping corresponded to those observed during testing.
Bakhle, Milind A.↗
Planar-Wing Flutter Analysis
Flutter Analysis System, FAST, is group of five programs that perform flutter analysis of single planar wing. Each program performs certain portions of flutter analysis and may be run sequentially or individually. Modular approach is very versatile and flexible. FAST uses natural vibration modes as input data and performs conventional V-g solution.
Desmarais, R. N.↗
Predicting Flutter Of A Propfan
Report discusses theoretical model and associated computer program for prediction of subsonic bending-torsion cascade flutter in propfans. Predictions of model compared with results of experiments. Additional parametric studies illustrate effects upon flutter speed of steady aeroelastic deformations, angle at which blade set, speed of rotation, structural damping, and number of vibrational modes. Calculations performed by parts of ASTROP computer code: ASTROP 2, based on two-dimensional, subsonic, unsteady aerodynamics; and ASTROP 3, based on three-dimensional, subsonic, steady and unsteady aerodynamics.
Kaza, K. R. V.↗
Alleviation of whirl-flutter on a joined-wing tilt-rotor aircraft configuration using active controls
The feasibility of using active controls to delay the onset of whirl-flutter on a joined-wing tilt rotor aircraft was investigated. The CAMRAD/JA code was used to obtain a set of linear differential equations which describe the motion of the joined-wing tilt-rotor aircraft. The hub motions due to wing/body motion is a standard input to CAMRAD/JA and were obtained from a structural dynamics model of a representative joined-wing tilt-rotor aircraft. The CAMRAD/JA output, consisting of the open-loop system matrices, and the airframe free vibration motion were input to a separate program which performed the closed-loop, active control calculations. An eigenvalue analysis was performed to determine the flutter stability of both open- and closed-loop systems. Sensor models, based upon the feedback of pure state variables and based upon hub-mounted sensors, providing physically measurable accelerations, were evaluated. It was shown that the onset of tilt-rotor whirl-flutter could be delayed from 240 to above 270 knots by feeding back vertical and span-wise accelerations, measured at the rotor hub, to the longitudinal cyclic pitch. Time response calculations at a 270-knot cruise condition showed an active cyclic pitch control level of 0.009 deg, which equates to a very acceptable 9 pound active-control force applied at the rotor hub.
Vanaken, Johannes M.↗
On curve veering and flutter of rotating blades
The eigenvalues of rotating blades usually change with rotation speed according to the Stodola-Southwell criterion. Under certain circumstances, the loci of eigenvalues belonging to two distinct modes of vibration approach each other very closely, and it may appear as if the loci cross each other. However, our study indicates that the observable frequency loci of an undamped rotating blade do not cross, but must either repel each other (leading to 'curve veering'), or attract each other (leading to 'frequency coalescence'). Our results are reached by using standard arguments from algebraic geometry--the theory of algebraic curves and catastrophe theory. We conclude that it is important to resolve an apparent crossing of eigenvalue loci into either a frequency coalescence or a curve veering, because frequency coalescence is dangerous since it leads to flutter, whereas curve veering does not precipitate flutter and is, therefore, harmless with respect to elastic stability.
Afolabi, Dare↗
Investigation of the Flow Physics Driving Stall-Side Flutter in Advanced Forward Swept Fan Designs
Flutter-free operation of advanced transonic fan designs continues to be a challenging task for the designers of aircraft engines. In order to meet the demands of increased performance and lighter weight, these modern fan designs usually feature low-aspect ratio shroudless rotor blade designs that make the task of achieving adequate flutter margin even more challenging for the aeroelastician. This is especially true for advanced forward swept designs that encompass an entirely new design space compared to previous experience. Fortunately, advances in unsteady computational fluid dynamic (CFD) techniques over the past decade now provide an analysis capability that can be used to quantitatively assess the aeroelastic characteristics of these next generation fans during the design cycle. For aeroelastic applications, Mississippi State University and NASA Glenn Research Center have developed the CFD code TURBO-AE. This code is a time-accurate three-dimensional Euler/Navier-Stokes unsteady flow solver developed for axial-flow turbomachinery that can model multiple blade rows undergoing harmonic oscillations with arbitrary interblade phase angles, i.e., nodal diameter patterns. Details of the code can be found in Chen et al. (1993, 1994), Bakhle et al. (1997, 1998), and Srivastava et al. (1999). To assess aeroelastic stability, the work-per-cycle from TURBO-AE is converted to the critical damping ratio since this value is more physically meaningful, with both the unsteady normal pressure and viscous shear forces included in the work-per-cycle calculation. If the total damping (aerodynamic plus mechanical) is negative, then the blade is unstable since it extracts energy from the flow field over the vibration cycle. TURBO-AE is an integral part of an aeroelastic design system being developed at Honeywell Engines, Systems & Services for flutter and forced response predictions, with test cases from development rig and engine tests being used to validate its predictive capability. A recent experimental program (Sanders et al., 2002) was aimed at providing the necessary unsteady aerodynamic and vibratory response data needed to validate TURBO-AE for fan flutter predictions. A comparison of numerical TURBO-AE simulations with the benchmark flutter data is given in Sanders et al. (2003), with the data used to guide the validation of the code and define best practices for performing accurate unsteady simulations. The agreement between the analyses and the predictions was quite remarkable, demonstrating the ability of the analysis to accurately model the unsteady flow processes driving stall-side flutter.
Sanders, Albert J.↗
Experimental transonic flutter characteristics of two 72 deg-sweep delta-wing models
Transonic flutter boundaries are presented for two simple, 72 deg. sweep, low-aspect-ratio wing models. One model was an aspect-ratio 0.65 delta wing; the other model was an aspect-ratio 0.54 clipped-delta wing. Flutter boundaries for the delta wing are presented for the Mach number range of 0.56 to 1.22. Flutter boundaries for the clipped-delta wing are presented for the Mach number range of 0.72 to 0.95. Selected vibration characteristics of the models are also presented.
Doggett, Robert V., Jr.↗
Ground Vibration Testing at NASA Armstrong, Emphasizing on Passive Aeroelastic Tailored Wing Ground Vibration Test Using Fixed Base Correction Method
How does experimental mechanics contribute to aircraft aeroelastic airworthiness? The aviation community is always improving analysis and testing techniques to realize quicker, cheaper, reliable solutions. A ground vibration test (GVT) is conducted to identify structural mode shapes, frequencies, and damping values to validate analytical models used for flutter analysis, which shows whether a structure has acceptable aeroelastic flutter margins for airworthiness. The FLL recently conducted a GVT of the Passive Aeroelastic Tailored (PAT) Wing using an experimental modal technique called Fixed Base Correction (FBC). The GVT objective was to obtain the PAT wing modal characteristics to compare test results with finite element model (FEM) results for the tow-steered wingbox.
loads testing↗
Unsteady flow past, and flexural flutter of, bodies of revolution in a supersonic stream <neustanovivsheyesya obtekaniye i izgibnyy flatter tel vrashcheniya v sverkazvukovom potoke<
Supersonic flow past bodies of revolution subject to elastic harmonic vibrations
SUPERSONIC FLOW↗
Bladed disk vibration
The objective was to better understand the vibratory response of bladed disk assemblies that occur in jet engines or turbopumps. Two basic problems were investigated: how friction affects flutter; and how friction, mistuning, and stage aerodynamics affect resonance. Understanding these phenomena allows a better understanding of why some stages have high vibratory stresses, how best to manage those stresses, and what to do about reducing them if they are too large.
Griffin, J. H.↗
Suppression of flutter
An active aerodynamic control system to control flutter over a large range of oscillatory frequencies is described. The system is not affected by mass, stiffness, elastic axis, or center of gravity location of the system, mode of vibration, or Mach number. The system consists of one or more pairs of leading edge and trailing edge hinged or deformable control surfaces, each pair operated in concert by a stability augmentation system. Torsion and bending motions are sensed and converted by the stability augmentation system into leading and trailing edge control surface deflections which produce lift forces and pitching moments to suppress flutter.
Nissim, E.↗
Laser Displacement Measurements of Fan Blades in Resonance and Flutter During the Boundary Layer Ingesting Inlet and Distortion-Tolerant Fan Test
NASA's Advanced Air Transport Technology Project is investigating boundary layer ingesting propulsors for future subsonic commercial aircraft to improve aircraft efficiency, thereby reducing fuel burn. To that end, a boundary layer ingesting inlet and distortion-tolerant fan stage was designed, fabricated, and tested within the 8' x 6' Supersonic Wind Tunnel at NASA Glenn Research Center. Because of the distortion in the air flow over the fan, the blades were designed to withstand a much higher aerodynamic forcing than for a typical clean flow. The blade response for several resonance modes were measured during start-up and shutdown, as well as at near 85% design speed. Flutter in the first bending mode was also observed in the fan at the design speed, at an off-design condition, although instabilities were difficult to instigate with this fan in general. Blade vibrations were monitored through twelve laser displacement probes that were placed around the inner circumference of the casing, at the blade leading and trailing edges. These probes captured the movement of all the blades during the entire test. Results are presented for various resonance mode amplitudes, frequencies and damping, as well as flutter amplitudes and frequency. Benefits and disadvantages of laser displacement probe measurements versus strain gage measurements are discussed.
NSMS↗
Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations
A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.
Reddy, Tondapu S.↗
Stability of a beam on an elastic foundation subjected to a follower force.
Discussion of a new aspect in the behavior of a cantilevered beam on an elastic foundation subjected to a follower force at its free end. The critical load for flutter is found to be independent of the foundation modulus which characterizes the Winkler-type elastic imbedding. The frequency of vibration of the beam increases with increasing foundation modulus, but the magnitude of the critical load is not affected. This result is valid for any 'tangency coefficient' value.
Smith, T. E.↗
Flight Flutter Testing of the P6M
On the P6M the shake behavior, i.e., the response to random excitation at subcritical speeds of lowly damped airplane modes, is as important as the actual flutter speed. The approach is to first study the problem by means of analyses and wind-tunnel tests. These predictions are compared with flight test data obtained by spectral analysis of tape recordings of the airplane vibration responses to random aerodynamic turbulence. A similar spectrum analysis approach was used in high speed wind-tunnel tests. A resonance excitation technique was developed for low speed wind-tunnel testing, and well defined V-g curves were obtained. The effect of various parameters on both shake and flutter of T-tails with and without dihedral were studied. Preliminary flight tests yielded good correlation; they also yielded interesting information concerning a low frequency transonic snaking mode, and excitation by shed vortices.
Kachadourian, G.↗
Instability modes of cantilevered bars induced by fluid flow through attached pipes.
Instability modes of cantilevered bars induced by fluid flow through attached pipes, examining cases of torsional and transverse flutter and torsional buckling
FLUID MECHANICS↗