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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Graphics Flutter Analysis Methods, an interactive computing system at Lockheed-California Company

An interactive computer graphics system, Graphics Flutter Analysis Methods (GFAM), was developed to complement FAMAS, a matrix-oriented batch computing system, and other computer programs in performing complex numerical calculations using a fully integrated data management system. GFAM has many of the matrix operation capabilities found in FAMAS, but on a smaller scale, and is utilized when the analysis requires a high degree of interaction between the engineer and computer, and schedule constraints exclude the use of batch entry programs. Applications of GFAM to a variety of preliminary design, development design, and project modification programs suggest that interactive flutter analysis using matrix representations is a feasible and cost effective computing tool.

Radovcich, N. A.↗
NASA NTRS1977

Simplified and refined structural modeling for economical flutter analysis and design

A coordinated use of two finite-element models of different levels of refinement is presented to reduce the computer cost of the repetitive flutter analysis commonly encountered in structural resizing to meet flutter requirements. One model, termed a refined model (RM), represents a high degree of detail needed for strength-sizing and flutter analysis of an airframe. The other model, called a simplified model (SM), has a relatively much smaller number of elements and degrees-of-freedom. A systematic method of deriving an SM from a given RM is described. The method consists of judgmental and numerical operations to make the stiffness and mass of the SM elements equivalent to the corresponding substructures of RM. The structural data are automatically transferred between the two models. The bulk of analysis is performed on the SM with periodical verifications carried out by analysis of the RM. In a numerical example of a supersonic cruise aircraft with an arrow wing, this approach permitted substantial savings in computer costs and acceleration of the job turn-around.

Ricketts, R. H.↗
NASA NTRS1995

Interactive flutter analysis and parametric study for conceptual wing design

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed on MathCad (trademark) platform for Macintosh, with integrated documentation, graphics, database and symbolic mathematics. The analysis method was based on nondimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The plots were compiled in a Vaught Corporation report from a vast database of past experiments and wind tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended Wing Body concept, proposed by McDonnell Douglas Corporation. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗
NASA NTRSDate not supplied

Classical Flutter Analysis of X-57 Aircraft Mod II, III, and IV Configurations

To support airworthiness assessment of the X-57 electric propulsion demonstrator aircraft, the National Aeronautics and Space Administration (NASA) completed classical flutter analysis of the Mod II, Mod III, and Mod IV aircraft configurations. Aeroelastic analysis was primarily performed using the ZAERO analysis code developed by Zona Technology. Supplemental computational fluid dynamics (CFD) flutter analysis for the Mod III and Mod IV configurations was performed using NASA’s FUN3D software to verify the aeroelastic behavior at deployed flaps conditions. The NASTRAN finite element models (FEMs) used for aeroelastic analysis were developed by NASA. The final Mod II FEM utilized shell elements for the wing and fuselage, and beam elements for the tail and wing control surfaces. For Mod III and Mod IV aircraft models, shell element wing FEMs developed throughout the Mod III/IV wing design cycle were utilized. The fuselage and empennage FEM components were shared between the Mod II, III, and IV aircraft models. ZAERO analyses predicted flutter boundaries were >60% beyond the X-57 flight-test envelope never exceed airspeed (V NE ) for all configurations. Aeroelastic Reynolds-averaged Navier–Stokes (RANS) CFD simulations using FUN3D of the Mod III/IV configurations predicted flap mode instability did not occur until at least speeds of 60% higher than the Mod III/IV maximum flap deployment airspeed (V FE ).

Keerti K. Bhamidipati↗
NASA NTRS1995

Flutter analysis of composite box beams

The dynamic aeroelastic instability of flutter is an important factor in the design of modern high-speed, flexible aircraft. The current trend is toward the creative use of composites to delay flutter. To obtain an optimum design, we need an accurate as well as efficient model. As a first step towards this goal, flutter analysis is carried out for an unswept composite box beam using a linear structural model and Theodorsen's unsteady aerodynamic theory. Structurally, the wing was modeled as a thin-walled box-beam of rectangular cross section. Theodorsen's theory was used to get 2-D unsteady aerodynamic forces, which were integrated over the span. A free-vibration analysis is carried out. These fundamental modes are used to get the flutter solution using the V-g method. Future work is intended to build on this foundation.

Hodges, Dewey H.↗
NASA NTRS1991

Flutter analysis of cascades using a two dimensional Euler solver

Flutter analysis of a cascade of blades in compressible flow is presented, with each blade of the cascade modeled as a typical section having pitching and plunging degrees of freedom. The aerodynamic forces are obtained from an unsteady, 2-D cascade solver based on the Euler equations. To reduce the computational time, an influence coefficient technique and a pulse response technique are also used to obtain the unsteady force coefficients for any frequency and phase angle. The predicted steady and unsteady aerodynamic forces for selected cascade geometries and flow conditions correlate well with the available experimental and analytical data.

Reddy, T. S. R.↗
NASA NTRS1982

NASTRAN documentation for flutter analysis of advanced turbopropellers

An existing capability developed to conduct modal flutter analysis of tuned bladed-shrouded discs was modified to facilitate investigation of the subsonic unstalled flutter characteristics of advanced turbopropellers. The modifications pertain to the inclusion of oscillatory modal aerodynamic loads of blades with large (backward and forward) varying sweep.

Elchuri, V.↗
NASA NTRS1977

State-space formulations for flutter analysis

Two state-space methods for true-damping flutter analysis are presented here. The aerodynamic matrix is assumed to be function of the complex reduced frequency p (off-the-imaginary axis aerodynamics) as the ones provided for instance by the computer code SOUSSA (Steady, Oscillatory and Unsteady, Subsonic and Supersonic Aerodynamics). This matrix is approximated by a third order polynomial or by a Pade's matrix approximant. Then the equations are cast into a suitable state space format including the Laplace transform of the space vector, a frequency-independent matrix, and the flight speed. The solution is then obtained by standard root-locus methods. Results are in good agreement with existing ones in a suitable range of the flutter reduced frequency. A discussion on spurious roots is also included.

Weiss, S. J.↗
NASA NTRS1982

NASTRAN flutter analysis of advanced turbopropellers

An existing capability developed to conduct modal flutter analysis of tuned bladed-shrouded discs in NASTRAN was modified and applied to investigate the subsonic unstalled flutter characteristics of advanced turbopropellers. The modifications pertain to the inclusion of oscillatory modal aerodynamic loads of blades with large (backward and forward) variable sweep. The two dimensional subsonic cascade unsteady aerodynamic theory was applied in a strip theory manner with appropriate modifications for the sweep effects. Each strip is associated with a chord selected normal to any spanwise reference curve such as the blade leading edge. The stability of three operating conditions of a 10-bladed propeller is analyzed. Each of these operating conditions is iterated once to determine the flutter boundary. A 5-bladed propeller is also analyzed at one operating condition to investigate stability. Analytical results obtained are in very good agreement with those from wind tunnel tests.

Elchuri, V.↗
NASA NTRS1992

Flutter analysis of a supersonic cascade in time domain using an ADI Euler solver

The aeroelastic stability of a two-dimensional cascade oscillating in supersonic axial flow is analyzed in the time domain. The aeroelastic model consists of a single degree of freedom typical section structural model for each blade of the cascade and an unsteady two-dimensional cascade aerodynamic model based on the Euler equations. The Euler equations are solved using a time accurate Alternating Direction Implicit (ADI) solution scheme. The aeroelastic equations are integrated in time. The effect of interblade phase angle is included in the aeroelastic analysis by an appropriate choice of initial and boundary conditions. Flutter predictions are obtained from the time response of a flat plate cascade in single degree of freedom pitching motion. The results correlate well with those obtained from a separate frequency domain flutter analysis for all values of interblade phase angles considered. Flutter results are then presented for cascades having airfoil sections representative of a supersonic throughflow fan. The validity of the time integration method for a cascade of airfoils at various interblade phase angles is demonstrated.

Reddy, T. S. R.↗
NASA NTRS1960

Subsonic Kernel-Function Flutter Analysis of a Highly Tapered Tail Surface and Comparison with Experimental Results

A flutter analysis employing the kernel function for three-dimensional, subsonic, compressible flow is applied to a flutter-tested tail surface which has an aspect ratio of 3.5, a taper ratio of 0.15, and a leading-edge sweep of 30 deg. Theoretical and experimental results are compared at Mach numbers from 0.75 to 0.98. Good agreement between theoretical and experimental flutter dynamic pressures and frequencies is achieved at Mach numbers to 0.92. At Mach numbers from 0.92 to 0.98, however, a second solution to the flutter determinant results in a spurious theoretical flutter boundary which is at a much lower dynamic pressure and at a much higher frequency than the experimental boundary.

Walberg, Gerald D.↗
NASA NTRS1973

Flutter analysis and testing of pairs of aerodynamically interfering delta wings

To examine the effect on flutter of the aerodynamic interference between pairs of closely spaced delta wings, several structurally uncoupled 1/80th-scale models were studied by experiment and analysis. Flutter test boundaries run in a 26-in transonic blowdown wind tunnel were compared with subsonic analytical results generated using the doublet lattice method. Trends for several combinations of vertical and longitudinal wing separation showed that flutter speeds can be significantly lowered in closely spaced configurations. For some configurations, a new flutter mechanism, characterized by coupling of the flexible modes from both surfaces at a distinctive flutter frequency, was predicted and observed.

Chipman, R. R.↗
NASA NTRS2011

Reduced Uncertainties in the Flutter Analysis of the Aerostructures Test Wing

Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. A test validated finite element model can provide a reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown prior to flight flutter testing. Minimizing the difference between numerical and experimental results is a type of optimization problem. Through the use of the National Aeronautics and Space Administration Dryden Flight Research Center's (Edwards, California) multidisciplinary design, analysis, and optimization tool to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes are matched to the target data, and the mass matrix orthogonality is retained. The approach in this study has been applied to minimize the model uncertainties for the structural dynamic model of the aerostructures test wing, which was designed, built, and tested at the National Aeronautics and Space Administration Dryden Flight Research Center. A 25 percent change in flutter speed has been shown after reducing the uncertainties.

Pak, Chan-Gi↗
NASA NTRS2010

Reduced Uncertainties in the Flutter Analysis of the Aerostructures Test Wing

Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. A test validated finite element model can provide a reliable flutter analysis to define the flutter placard speed to which the aircraft can be flown prior to flight flutter testing. Minimizing the difference between numerical and experimental results is a type of optimization problem. Through the use of the National Aeronautics and Space Administration Dryden Flight Research Center s (Edwards, California, USA) multidisciplinary design, analysis, and optimization tool to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes are matched to the target data and the mass matrix orthogonality is retained. The approach in this study has been applied to minimize the model uncertainties for the structural dynamic model of the aerostructures test wing, which was designed, built, and tested at the National Aeronautics and Space Administration Dryden Flight Research Center. A 25-percent change in flutter speed has been shown after reducing the uncertainties

Pak, Chan-gi↗