Abstract
It is important to account for uncertainties in aeroelastic response when designing and certifying aircraft. However, aeroelastic uncertainties are particularly challenging to quantify, since dynamic stability is a binary property (stable or unstable) that may be sensitive to small variations in system parameters. To correctly discern stability, the interactions between fluid and structure must be accurately captured. Such interactions involve an energy flow through the interface, which if unbalanced, can destablize the structure. With conventional computational techniques, the consequences of imbalance may require large simulation times to discern, and evaluating the dependence of stability on numerous system parameters can become intractable. In this chapter, the challenges in quantifying aeroelastic uncertainties will be explored and numerical methods will be described to decrease the difficulty of quantifying aeroelastic uncertainties and increase the reliability of aircraft structures subjected to airloads. A series of aeroelastic analyses and reliability studies will be carried out to illustrate key concepts.
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Allen, M., Maute, K.: Reliability-Based Design Optimization of Aeroelastic Structures. Structural and Multidisciplinary Optimization 27(4), 228–242 (2004)
Allen, M., Maute, K.: Reliability-Based Shape Optimization of Structures Undergoing Fluid-Structure Interaction Phenomena. Computer Methods in Applied Mechanics and Engineering 194(30), 3472–3495 (2005)
Ashley, H., Zartarian, G.: Piston Theory - A New Aerodynamic Tool for the Aeroelastician. Journal of the Aeronautical Sciences 23(12), 1109–1118 (1956)
Badcock, K., Woodgate, M.: Bifurcation Prediction of Large-Order Aeroelastic Models. AIAA Journal 48(6), 1037–1046 (2010)
Badcock, K., Timme, S., Marques, S,. Khodaparast, H., Prandina, M., Mottershead, J., Swift, A., Da Ronch, A., Woodgate, M.: Transonic Aeroelastic Simulation for Instability Searches and Uncertainty Analysis. Progress in Aerospace Sciences 47(2), 392–423 (2011)
Basudhar, A., Missoum, S.: Update of Explicit Limit State Functions Constructed Using Support Vector Machines. AIAA 2007-1872, April (2007)
Beloiu, D., Ibrahim, R., Pettit, C.: Influence of Boundary Conditions Relaxation on Panel Flutter with Compressive In-Plane Loads. Journal of Fluids and Structures 21(2), 743–767 (2005)
Bendiksen, O.O.: Review of Unsteady Transonic Aerodynamics: Theory and Applications. Progress in Aerospace Sciences (47), 136–167 (2011)
Bendiksen, O.O.: Unsteady Aerodynamics and Flutter Near Mach 1: Aerodynamic and Stability Reversal Phenomena. IFASD 2011-091, Paris, June (2011)
Beran, P.S., Lucia, D.J.: A Reduced Order Cyclic Method for Computation of Limit Cycles. Nonlinear Dynamics 39(1–2), 143–158 (2005)
Beran, P.S., Morton, S.A.: A Continuation Method for the Calculation of Airfoil Flutter Boundaries. Journal of Guidance, Control and Dynamics 20(6), 1165–1171 (1997)
Beran, P.S.: Computation of Limit-Cycle Oscillation Using a Direct Method. AIAA 1999-1462, April (1999)
Beran, P.S., Pettit, C.L., Millman, D.R.: Uncertainty Quantification of Limit-Cycle Oscillations. Journal of Computational Physics 217(1), 217–247 (2006)
Beran, P.S.: A Domain-Decomposition Method for Airfoil Flutter Analysis. AIAA 1998-506, January (1998)
Bisplinghoff, R., Ashley, H., Halfman, R.: Aeroelasticity. Addison-Wesley, Cambridge, MA (1955)
Chandiramani, N., Librescu, L., Plaut, R.: Flutter of Geometrically-Imperfect Shear-Deformable Laminated Flat Panels Using Non-Linear Aerodynamics. Journal of Sound and Vibration 192(1), 79–100 (1996)
Chen, P.C.: Damping Perturbation Method for Flutter Solution: The g-method. AIAA Journal 38(9), (2000)
Choi, S-K., Grandhi, R.V., Canfield, R.A.: Reliability-based Structural Design. Springer, London (2007)
Denegri, C.: Limit Cycle Oscillation Flight Test Results of a Fighter with External Stores. Journal of Aircraft 37(5), 761–769 (2000)
Dribusch, C., Missoum, S., Beran, P.: A Multifidelity Approach for the Construction of Explicit Decision Boundaries: Application to Aeroelasticity. Structural Multidisciplinary Optimization 42(5), 693–705 (2010)
Dowell, E., Edwards, J., Strganac, T.: Nonlinear Aeroelasticity. Journal of Aircraft 40(5), 857–874 (2003)
Dowell, E.H.: Nonlinear Oscillations of a Fluttering Plate. AIAA Journal 4(7), 1267–1275 (1966)
Eldred, M., Bichon, B.: Second-Order Reliability Formulations in DAKOTA/UQ. AIAA 2006-1828 (2006)
Franklin, J.N.: Matrix Theory. Prentice-Hall, Englewood Cliffs (1968)
Ghommem, M., Hajj, M., Nayfeh, A.: Uncertainty Analysis near Bifurcation of an Aeroelastic System. Journal of Sound and Vibration 329(16), 3335–3347 (2010)
Gilliatt, H., Strganac, T., Kurdila, A.: An Investigation of Internal Resonance in Aeroelastic Systems. Nonlinear Dynamics 31, 1–22 (2003)
Griewank, A., Reddien, G.: The Calculation of Hopf Points by a Direct Method. IMA Journal of Numerical Analysis 3(1), 295–303 (1983)
Grigoriu, M.: Stochastic Calculus: Applications in Science and Engineering. Birkhauser, Boston (2002)
Koyluoglu, H., Nielsen, S.: New Approximations for SORM Integrals. Structural Safety, 13(6), 235–246 (1994)
Melchers, R.: Structural Reliability: Analysis and Prediction. Wiley, Chichester, UK (1987)
Mignolet, M.P., Chen, P.C.: Aeroelastic Analyses with Uncertainty in Structural Properties. Proceedings of the AVT-147 Symposium: Computational Uncertainty in Military Vehicle Design, Athens, Greece, Dec (2007)
Morton, S., Beran, P.: Hopf-Bifurcation Analysis of Airfoil Flutter at Transonic Speeds. Journal of Aircraft 36(2), 421–429 (1999)
Murthy, D., Haftka, R.: Derivatives of Eigenvalues and Eigenvectors of a General Complex Matrix. International Journal for Numerical Methods in Engineering 26(2), 293–311 (1988)
Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics. Wiley, New York (1995)
Nayfeh, A., Ghommem, M., Hajj, M.: Normal Form Representation of the Aeroelastic Response of the Goland Wing. Nonlinear Dynamics, DOI: 10.1007/s11071-011-0111-6 (2011).
Nikbay, M., Fakkusoglu, N., Kuru, M.: Reliability-Based Aeroelastic Optimization of a Composite Aircraft Wing via Fluid-Structure Interaction of High Fidelity Solvers. Materials Science and Engineering 10(1), 1–10 (2010)
Paolone, A., Vasta, M., Luongo, A.: Flexural-Torsional Bifurcations of a Cantilever Beam Under Potential and Circulatory Forces II. Post-Critical Analysis. International Journal of Non-Linear Mechanics 41(4), 595–604 (2006)
Pettit, C.L., Beran, P.S.: Convergence Studies of Wiener Expansions for Computational Nonlinear Mechanics. AIAA 2006-1993, May (2006)
Pettit, C., Grandhi, R.: Optimization of a Wing Structure for Gust Response and Aileron Effectiveness. Journal of Aircraft 40(6), 1185–1191 (2003)
Schijve, J.: Fatigue of Aircraft Materials and Structures. International Journal of Fatigue 16(1), 21–32 (1994)
Stanford, B., Beran, P.: Optimal Structural Topology of a Plate-Like Wing for Subsonic Aeroelastic Stability. Journal of Aircraft 48(4), 1193–1203 (2011)
Stanford, B., Beran, P.: Computational Strategies for Reliability-Based Structural Optimization of Aeroelastic Limit Cycle Oscillations. Structural and Multidisciplinary Optimization 45(1), 83–99 (2012)
Stanford, B., Beran, P.: Direct Flutter and Limit Cycle Computations of Highly-Flexible Wings for Efficient Analysis and Optimization. Journal of Fluids and Structures (in review), (2011)
Timme, S., Marques, S., Badcock, K.: Transonic Stability Analysis Using a Kriging-Based Schur Complement Formulation. AIAA 2010-8228, August (2010)
Acknowledgements
The authors wish to thank Prof. Ramana Grandhi (Wright State University) for many discussions that were helpful in the preparation of this manuscript, Dr. Chris Koehler (Universal Technology Corporation) for assistance in developing manuscript graphics, and Dr. Manav Bhatia (Universal Technology Corporation) for reviewing the manuscript. This work was sponsored by the Air Force Office of Scientific Research under Laboratory Task 03VA01COR (monitored by Dr. Fariba Fahroo).
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Beran, P., Stanford, B. (2013). Uncertainty Quantification in Aeroelasticity. In: Bijl, H., Lucor, D., Mishra, S., Schwab, C. (eds) Uncertainty Quantification in Computational Fluid Dynamics. Lecture Notes in Computational Science and Engineering, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-00885-1_2
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