The nonlinear panel flutter problem solved by Dowell in 1966 is used to investigate the new application of the proper orthogonal decomposition model reduction technique to aeroelastic analysis. Emphasis is placed on the nonlinear structural dynamic equations with nonconservative forcing modeled assuming a supersonic, inviscid flow. Here the aeroelastic coupled equation is presented in discrete form using a finite difference approach, and subsequently in state space form, to be integrated as a set of first order differential equations. In this paper, a POD approach is developed for generalized second-order differential equations; however, the application of POD to the governing equations in state space form is also discussed. This study compares the results and effectiveness of the model reduction technique for integration of the full set of degrees of freedom. The solution is compared to Dowell’s classic results which forms the base reference for the model reduction study. The reduced order model is then created from the full simulation model. Accuracy of the solution, reduced computational time, limits of stability, and the strengths and weaknesses of the model reduction are investigated.

Issue Section:
Technical Papers
Keywords:
elasticity, aerodynamics, supersonic flow, vibrations, finite difference methods
Topics:
Flutter (Aerodynamics), Principal component analysis, Stability, Differential equations, Degrees of freedom
1.
Dowell
,
E. H.
,
1966
, “
Nonlinear Oscillations of a Fluttering Plate
,”
AIAA J.
,
4
(
7
), July, pp.
1267
–
1275
.
2.
Dowell, E. H., 1975, Aeroelasticity of Plates and Shells, chap. 3: “Nonlinear Theoretical Aeroelastic Models,” pp. 35–36.
3.
Slater
,
J.
,
Petit
,
C.
, and
Beran
,
P.
,
2002
, “
In-Situ Subspace Evaluation in Reduced Order Modeling
,”
Shock Vib.
,
9
, pp.
105
–
122
.
4.
Beran, P., and Silva, W., 2001, “Reduced-Order Modeling: New Approaches for Computational Physics,” 39th Aerospace Sciences Meeting & Exhibit, No. 2001-0853, Reno, NV, Jan 2001.
5.
Romanowski, M., 1996, “Reduced Order Unsteady Aerodynamic and Aeroelastic Models Using Karhunen-Loeve Eigenmodes,” Part 3, Bellevue, WA, Sept., AIAA 96-3981-CP.
6.
Holmes, P., Lumley, J., and Berkooz, G., 1996, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press.
7.
Park
,
H.
, and
Lee
,
M.
,
1998
, “
An Efficient Method for Solving the Navier-Stokes Equations for Flow Control
,”
Int. J. Numer. Methods Eng.
,
41
, pp.
1133
–
1151
.
8.
Hall, K., Thomas, J., and Dowell, E., 1999, “Reduced-Order Modeling of Unsteady Small-Disturbance Flows Using a Frequency-Domain Proper Orthogonal Decomposition Technique,” No. 0655, Jan.
9.
Beran, P., and Petit, C., 2001, “Prediction of Nonlinear Panel Response Using Proper Orthogonal Decomposition,” 42nd Structures, Structural Dynamics, and Materials Conference, No. 2001-1292, Seattle, WA, Apr.
10.
Krysl
,
P.
,
Lall
,
S.
, and
Marsden
,
J.
,
2001
, “
Dimensional Model Reduction in Non-Linear Finite Element Dynamics of Solids and Structures
,”
Int. J. Numer. Methods Eng.
,
51
(
4
), pp.
479
–
504
.
11.
Mortara, S. A., Slater, J. C., and Beran, P. S., 2000, “A Proper Orthogonal Decomposition Technique for the Computation of Nonlinear Panel Response,” 41st Structures, Structural Dynamics, and Materials Conference, No. 2000-1936, Atlanta, GA, Apr.
12.
Beran, P., Huttsel, L., and Buxton, B., 1999, “Computational Aeroelasticity Techniques for Viscous Flow,” CEAS/AIAA/CASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics, Williamsburg, Virginia, June.
13.
Selvam, R., and Visbal, M., 1998, “Computation of Nonlinear Viscous Panel Flutter Using a Fully-Implicit Aeroelastic Solver,” Long Beach, CA, April, AIAA-98-1844.
14.
Selvam, R., 1998, “Computer Modeling of Nonlinear Viscous Panel Flutter,” Tech. rep., ARFL, WPAFB, OH, August.
15.
O’Callahan, J., Avitabile, P., and Riemer, R., 1989, “System Equivalent Reduction Expansion Process (SEREP),” Proceedings of the 7th International Modal Analysis Conference, Las Vegas, Nevada, February.
16.
Inman, D. J., 1996, Engineering Vibration, Prentice Hall Chap. 4.3.
Copyright © 2004
 by ASME
You do not currently have access to this content.