Summary
Active aeroelastic control is a recently emerging technology aimed at providing solutions to a large class of problems involving the aeronautical/aerospace flight vehicle structures that are prone to instability and catastrophic failures, and to oscillations that can yield structural failure by fatigue. In order to prevent such damaging phenomena to occur, the linear/nonlinear aeroelastic control technology should be applied. Its goals are among others: (i) to alleviate and even suppress the vibrations appearing in the subcritical flight speed range, (ii) to enlarge the flight envelope by increasing the flutter speed, and (iii) to enhance the post-flutter behavior by converting the unstable limit cycle oscillation to a stable one. A short review of the available control techniques and capabilities is presented first. Attention is focused on the open/closed-loop of 2D and 3D lifting surfaces as well as on panels exposed to supersonic flowfields. A number of concepts involving various control methodologies, such as proportional, velocity, linear quadratic regulator, modified bang-bang, sliding mode observer, time-delay control, fuzzy, etc., as well as results obtained with such controls are presented. Emphasis is placed on theoretical and numerical results obtained with the various control strategies that are considered in a comparative way. Finally, conclusions and directions for further work are presented.
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References
V. Mukhopadhyay (1995) ArticleTitleFlutter suppression control law design and testing for the active flexible wing J Aircraft (Special Adaptive Flexible Wing Issue) 32 45–51
V. Mukhopadhyay (2003) ArticleTitleHistorical perspective on analysis and control of aeroelastic responses J. Guidance Control Dyn. 26 673–684
Librescu, L, Na, S. S., Marzocca, P., Chung, C.-H., Jeong, I.-J.: Active aeroelastic control of 2- D wing-flap systems in a compressible/incompressible flow field and exposed to blast pulses IMECE 2003-43392. In: Proc. 2003 ASME Int. Mechanical Engineering Congress and Exposition, Washington, D.C, pp. 15–21, November 2003
L. Librescu S. S. Na P. Marzocca C. Chung M. Kwak (2005) ArticleTitleActive aeroelastic control of 2D wing flap systems operating in an incompressible flowfield and impacted by a blast pulse J. Sound Vibr. 83 685–706 Occurrence Handle10.1016/j.jsv.2004.05.010
R. C. Scott S. T. Hoadley C. D. Wieseman M. H. Durham (2001) ArticleTitleBenchmark active controls technology model aerodynamic data J. Guidance Control Dyn. 23 914–921
J. Block T. M. Strganac (1998) ArticleTitleApplied active control for a nonlinear aeroelastic structure J. Guidance Control Dyn. 21 838–845
J. Ko A. J. Kurdila T. W. Strganac (1997) ArticleTitleNonlinear control of a prototypical wing section with torsional nonlinearity J. Guidance Control Dyn. 20 1181–1189
Ko, J., Kurdila, A. J., Strganac, T. W.: Nonlinear adaptive control of an aeroelastic system via geometric methods. AIAA Paper 98-1795. In: Proc. 39th AIAA/ASME/ASCE/AHS/ACS Structures, Structural Dynamics and Materials Conf., Long Beach, CA, April 1998
T. W. Strganac J. Ko D. E. Thompson A. J. Kurdila (2000) ArticleTitleIdentification and control of limit cycles oscillations in aeroelastic systems J. Guidance Control Dyn. 23 1127–1133
P. Marzocca L. Librescu W. A. Silva (2002) ArticleTitleFlutter, post-flutter and control of a supersonic 2-D lifting surface J. Guidance Control Dyn. 25 962–970
Y. Yuan P. Yu L. Librescu P. Marzocca (2004) ArticleTitleAeroelasticity of time-delayed feedback control of two-dimensional supersonic lifting surfaces J. Guidance Control Dyn. 27 795–803
P. Marzocca L. Librescu W. A. Silva (2004) ArticleTitleTime-delay effects on linear/nonlinear feedback control of simple aeroelastic systems J. Guidance Control Dyn. 28 53–62
Marzocca, P., Librescu, L., Silva, W. A.: Open/closed-loop nonlinear aeroelasticity for airfoils via Volterra series approach. AIAA Paper 2002-1484. In: Proc. 43rd AIAA/ASME/ASCE/AHS/ ASC Structures, Structural Dynamics and Materials Conf., Denver, CO, April 2002. Also appeared as J. Fluids Struct. 20, 197–215 (2005)
Librescu, L., Marzocca, P., Silva, W. A.: Time-delay feedback aeroelastic control of 2-D lifting surfaces. IMECE 2002-32971. In: Proc. 5th Int. Symp. on Fluid-structure Interaction, Aeroelasticity, Flow-induced Vibration and Noise 2002 ASME Int. Mechanical Engineering Congress and Exposition, New Orleans, LA, November 2002 (also appeared as J. Fluids Struct 20, 197–215, 2005)
Marzocca, P., Librescu, L., Silva, W. A.: Nonlinear time-delayed feedback control of aeroelastic systems: a functional approach. AIAA Paper 2003-1867. In: Proc 44th AIAA/ASME/ ASCE/ ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA, April 2003
Yuan, Y., Yu, P., Librescu, L., Marzocca, P.: Analysis of a 2D supersonic lifting surface with time-delayed feedback control. AIAA Paper 2003-1733. In: Proc. 44th AIAA/ASME/ASCE/ ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA, April 2003
M. Ramesh S. Narayanan (2001) ArticleTitleControlling chaotic motions in a two-dimensional airfoil using time-delayed feedback J. Sound Vibr. 239 1037–1049 Occurrence Handle10.1006/jsvi.2000.3181
W. Xing S. N. Singh (2000) ArticleTitleAdaptive output feedback control of a nonlinear aeroelastic structure J. Guidance Control Dyn. 23 1109–1116
R. Zhang S. N. Singh (2001) ArticleTitleAdaptive output feedback control of an aeroelastic system with unstructured uncertainties J. Guidance Control Dyn. 24 502–509
H. Özbay G. R. Bachmann (1994) ArticleTitleController design for a two-dimensional thin airfoil flutter suppression J. Guidance Control Dyn. 17 722–728
Gern, F.H., Librescu, L. Synergistic interaction of aeroelastic tailoring and boundary moment control on aircraft wing flutter, NASA/CP 1999 209136/PT2, 719 733. In: Proc. CEAS/AIAA/ ICASE/NASA Int. Forum on Aeroelasticity and Structural Dynamics, June 1999
L. Librescu L. Meirovitch O. Song (1996) ArticleTitleRefined structural modeling for enhancing vibrations and aeroelastic characteristics of composite aircraft wings La Recherche Aérospatiale 1 23–35
L. Librescu L. Meirovitch O. Song (1996) ArticleTitleIntegrated structural tailoring and control using adaptive materials for advanced aircraft wings J. Aircraft 33 203–213
Librescu, L, Na, S. S., Marzocca, P., Chung, C., Kwak, M. K.: Flutter instability and aeroelastic response of aircraft wing section with a flap in an incompressible flow. IMECE 2002-32983. In: Proc. 5th Int. Symp. on Fluid-structure Interaction, Aeroelasticity, Flow-induced Vibration and Noise, 2002 ASME Int. Mechanical Engineering Congress and Exposition, 17–22 November 2002, New Orleans, LA
Librescu, L. Na, S. S., Marzocca, P., Chung, C., Kwak, M. K.: Active aeroelastic control of 2-D wing-flap systems in an incompressible flowfield. AIAA Paper 2003-1414. In: Proc. 44th AIAA/ ASE/ASCE/ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA., April 7–10, 2003
Na, S.S., Librescu, L., Marzocca, P., Chung, C.: Aeroelastic response of flapped wing system using robust control methodology. AIAA Paper 2004-1673. In: Proc. 45th AIAA/ASME/ ASCE/ASC Structures, Structural Dynamics and Materials Conf., Palm Springs, CA, 19–22 April 2004
Heeg, J., Scott, R. C., McGowan, A. M. R.: Aeroelastic research: using smart structures concepts, aeroelasticity and fluid structure interaction problems. In: Friedmann P.P., Chang J.C.I. (ed). AD-44. American Society of Mechanical Engineers, New York, pp. 161–173, 1994
McGowan, A. M. R., Washburn, A. E., Horta, L. G., Bryant, R. G., Cox, D. E., Siochi, E. J., Padula, S. L., Holloway, N. M.: Recent results from NASA’s morphing project. In: Proc. 9th Int Symp. on Smart Structures and Materials, Society of Photo Optical Instrumentation Engineers, San Diego, CA, Paper 4698-11, March 2002
Olds, S.D.: Modeling and LQR control of a two-dimensional airfoil. MS thesis, Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, April 1997
York, D. L.: Analysis of flutter and flutter suppression via an energy method. MS Thesis, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, May 1980
D. J. Inman (2000) ArticleTitleActive modal control for smart structures Phil. Trans. Math. Phys. Engng. Sci. 359 205–219 Occurrence Handle10.1098/rsta.2000.0721
M. Tadi (2003) ArticleTitleState dependent Riccati equation for control of aeroelastic flutter J. Guidance Control Dyn. 26 914–917
Djayapertapa, L., Allen, C.B.: Numerical simulation of active control of transonic flutter. In: Proc. 23rd ICAS Congress, Toronto, 411.1–411.10, 2002
D. M. Guillot P. P. Friedmann (2000) ArticleTitleFundamental aeroservoelastic study combining unsteady computational fluid mechanics with adaptive control J. Guidance Control Dyn. 23 1117–1126
P. Friedmann D. Guillot E. Presente (1997) ArticleTitleAdaptive control of aeroelastic instabilities in transonic flow and its scaling J. Guidance Control Dyn. 20 1190–1199
S. Chiu S. Chand D. Moore A. Chaudhury (1991) ArticleTitleFuzzy logic for control of roll and moment for a flexible wing aircraft IEEE Control Sys. Mag. 11 42–48 Occurrence Handle10.1109/37.88591
T. A. Weisshaar R. J. Ryan (1986) ArticleTitleControl of aeroelastic instabilities through stiffness cross coupling J. Aircraft 23 148–154
Anderson, K. R., White, K., Neal, J.: Survey of active aeroelastic control for flutter suppression Paper IMECE2004-60458 Proc. IMECE2004: 2004 ASME Int. Mechanical Engineering Congress and RD&D Expo, Anaheim, CA, November 13–19, 2004
McGowan, A. M. R.: An examination of applying shunted piezoelectrics to reduce aeroelastic response. NASA LaRC, May 2003; available at http://techreports.larc.nasa.gov/ltrs/PDF/1999/ mtg/NASA-99-ceas-arm.pdf
Librescu, L., Marzocca, P.: Flutter and post-flutter control of geometrically nonlinear panels operating in a supersonic / hypersonic flow field. IMECE2004-61373: Proc. IMECE2004, 2004 ASME Int. Mechanical Engineering Congress and Exposition, Session: AMD-10 B Multi-field Coupling in Dynamic Systems and Control, Anaheim, CA, November 13–19, 2004
P. Marzocca L. Librescu G. Chiocchia (2001) ArticleTitleAeroelastic response of a 2D lifting surfaces to gust and arbitrary explosive loading signatures Int. J. Impact Engng. 25 41–65 Occurrence Handle10.1016/S0734-743X(00)00033-6
R. H. Scanlan R. Rosenbaum (1951) Introduction to the study of aircraft vibration and flutter Macmillan New York
E. H. Dowell (1978) A modern course in aeroelasticity Sijthoff and Noordhoff The Netherlands
R. L. Bisplinghoff H. Ashley R. L. Halfman (1996) Aeroelasticity Dover New York
P. Marzocca L. Librescu W. A. Silva (2002) ArticleTitleAeroelastic response of nonlinear wing section by functional series technique AIAA J. 40 813–824
V. V. Bolotin (1963) Nonconservative problems of the theory of elastic stability Macmillan New York 274–312
Librescu, L.: Aeroelastic stability of orthotropic heterogeneous thin panels in the vicinity of the flutter critical boundary. J. Mécanique 4, 51–76 (1965) (Part I); 6, 133–152 (1967) (Part II)
L. Librescu (1975) Elastostatics and kinetics of anisotropic and heterogeneous shell-type structures, aeroelastic stability of anisotropic multilayered thin panels Noordhoff Leyden 106–158
E. H. Dowell (Eds) (1974) Aeroelasticity of plates and shells Kluwer Dordrecht
P. Friedmann M. Hanin (1968) ArticleTitleSupersonic nonlinear flutter of orthotropic or isotropic panels with arbitrary flow direction Israel J. Technol. 6 46–57
B. H. K. Lee S. J. Price Y. S. Wong (1999) ArticleTitleNonlinear aeroelastic analysis of airfoils: bifurcation and chaos Progr. Aerosp. Sci. 35 205–334 Occurrence Handle10.1016/S0376-0421(98)00015-3
I. Lee S. H. Kim (1995) ArticleTitleAeroelastic analysis of a flexible control surface with structural nonlinearity J. Aircraft 32 868–874
C. Mei (1977) ArticleTitleA finite element approach of nonlinear panel flutter AIAA J. 15 1107–1110
L. Morino (1969) ArticleTitleA perturbation method for treating nonlinear panel flutter problems AIAA J. 7 405–411
F Mastroddi L. Morino (1996) ArticleTitleLimit-cycle taming by nonlinear control with application to flutter Aeronaut J. 100 389–396
Hopf, E.: Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems (Bifurcation of a periodic solution from a stationary solution of a system of differential equations.) Ber. Math. Phys. Klasse der sächsischen Akad. Wiss. (Leipzig) 94, 3–32 (1942).
P. J. Holmes (1977) ArticleTitleBifurcations to divergence and flutter in flow-induced oscillations: a finitedimensional analysis J. Sound Vibr. 53 471–503 Occurrence Handle10.1016/0022-460X(77)90521-1
J. Guckenheimer P. Holmes (1986) Nonlinear oscillations, dynamical systems, and bifurcations of vector field Springer New York
L. Librescu (1981) On the effect of physical nonlinearities in the aeroelastic stability problem of supersonic panels J. Hult J. Lemaitre (Eds) Physical nonlinearities in structural analysis Springer Berlin 156–159
L. Librescu G. Chiocchia P. Marzocca (2003) ArticleTitleImplications of cubic physical / aerodynamic nonlinearities on the character of the flutter instability boundary Int. J. Non-Linear Mech. 38 173–199 Occurrence Handle10.1016/S0020-7462(01)00054-3
Breitbach, E. J.: Effects of structural nonlinearities on aircraft vibration and flutter. AGARD TR 665 (1977), and In: Proc. 34th Structures and Materials AGARD Panel Meeting, Voss, Norway, AGARD Report 554 (1977).
L. Librescu P. Marzocca W. A. Silva (2002) ArticleTitleSupersonic/hypersonic flutter and postflutter of geometrically imperfect circular cylindrical panels J. Spacecraft Rockets 39 802–812
N. K. Chandiramani L. Librescu R. Plaut (1996) ArticleTitleFlutter of geometrically imperfect sheardeformable laminated flat panels using nonlinear aerodynamics J. Sound Vibr. 192 79–100 Occurrence Handle10.1006/jsvi.1996.0177
O. O. Bendiksen (2004) ArticleTitleModern developments in computational aeroelasticity Proc. I MECH E Part G, J. Aerospace Engng. 218 157–177
P. P. Friedmann (1999) ArticleTitleRenaissance of aeroelasticity and its future J. Aircraft 36 105–121
E. Livne (2003) ArticleTitleFuture of airplane aeroelasticity J. Aircraft 40 1066–1092
E. Dowell J. Edwards T. Strganac (2003) ArticleTitleNonlinear aeroelasticity J. Aircraft 40 857–874
R. Lind M. Brenner (1999) Robust aeroservoelastic stability analysis Springer London
J. M. Barker G. J. Balas (2000) ArticleTitleComparing linear parameter-varying gain-scheduled control techniques for active flutter suppression J. Guidance Control Dyn. 23 948–955
R. C. Scott L. E. Pado (2000) ArticleTitleActive control of wind-tunnel model aeroelastic response using neural networks J. Guidance Control Dyn. 23 1100–1108
S. S. Na L. Librescu (2000) ArticleTitleOptimal vibration control of thin walled anisotropic cantilevers exposed to blast loading J. Guidance Control Dyn. 23 491–500
S. S. Na L. Librescu (2000) ArticleTitleOptimal dynamic response control of adaptive thin walled cantilevers carrying heavy stores and exposed to blast pulses J. Intell. Mater. Struct. 11 703–712 Occurrence Handle10.1177/104538900772663928
S. S. Na L. Librescu (2002) ArticleTitleOptimal dynamic response control of elastically tailored nonuniform thin walled adaptive beams J. Aircraft 39 469–479
S. S. Na L. Librescu J. H. Shim (2004) ArticleTitleModified bang-bang vibration control applied to adaptive thin-walled beam cantilevers AIAA J. 42 1717–1721
J. C. Bruch SuffixJr. J. M. Sloss S. Adali I. S. Sadek (1999) ArticleTitleModified bang-bang piezoelectric control of vibrating beams J. Smart Mater. Struct. 8 647–653 Occurrence Handle10.1088/0964-1726/8/5/315
Na, S., Park, C., Kim, M.-H., Librescu, L., Marzocca, P., Jeong, I.-J.: Aeroelastic response of flapped wing systems using multiobjective state feedback methodology. ICAST 2004, 15th Int Conf. on Adaptive Structures and Technologies, Bar Harbor, Maine, October 25–27, 2004.
E. Albano W. P. Rodden (1969) ArticleTitleA doublet-lattice method for calculating lift distribution on oscillating surfaces in subsonic flows AIAA J. 7 279–285
Tobak, M.: On the use of the indicial function concept in the analysis of unsteady motion of wings and wing-tail combinations. NASA R-1188, 1954.
Marzocca, P., Librescu, L., Kim, D.-H., Lee, I.: Linear/nonlinear unsteady aerodynamic modeling of 2-D lifting surfaces via a combined CDF/analytical approach. AIAA Paper 2003– 925, 44th AIAA/ASME/ASCE/ASC Structures, Structural Dynamics and Materials Conf., Norfolk, VA, April 7–10, 2003.
Kim, D., Lee, I., Marzocca, P., Librescu, L.: Linear/nonlinear aeroelastic computation of 2-D lifting surfaces using a combined CFD/analytical approach. AIAA Paper 2004–1756, 45th AIAA/ASME/ ASCE/ASC Structures, Structural Dynamics and Materials Conf., Palm Springs, CA, 19–22 April 2004.
Leishman, J. G.: Unsteady aerodynamics. In: Principles of helicopter aerodynamics, chap. 8, pp. 302–377. Cambridge: Cambridge University Press 2000.
Marzocca, P., Librescu, L., Chiocchia, G.: Unsteady aerodynamics in various flight speed regimes for flutter/dynamic response analyses. AIAA Paper 2000–4299, Proc. 18th AIAA Applied Aerodynamic Conf., Denver, CO, August 14–17, 2000.
P. Marzocca L. Librescu G. Chiocchia (2002) ArticleTitleAeroelastic response of a 2-D airfoil in compressible flight speed regimes exposed to blast loadings Aerosp. Sci. Technol. 6 259–272 Occurrence Handle10.1016/S1270-9638(02)01169-0
Mazelsky, B., Drischler, J. A.: Numerical determination of indicial lift and moment functions for a two-dimensional sinking and pitching airfoil at Mach numbers 0.5 and 0.6. NACA-TN-2739, July 1952.
Lomax, H.: Indicial aerodynamics, part II, chap. 6. AGARD Manual on Aeroelasticity, 1996.
Marzocca, P., Librescu, L., Chiocchia, G.: Aeroelasticity of two-dimensional lifting surfaces via indicial function approach. Aeronaut. J. 147–153 (2002).
Reisenthel, P. H.: Development of a nonlinear indicial model for maneuvering fighter aircraft AIAA Paper 96-0896, 34th Aerospace Sciences Meeting, Reno, NA, January 1996
R. C. Nelson A. Pelletier (2003) ArticleTitleThe unsteady aerodynamics of slender wings and aircraft undergoing large amplitude maneuvers Progr. Aerosp. Sci. 39 185–248 Occurrence Handle10.1016/S0376-0421(02)00088-X
J. Sitaraman J. D. Baeder (2004) ArticleTitleComputational-fluid-dynamics-based enhanced indicial aerodynamic models J. Aircraft 41 798–810
G. P. Guruswamy (1990) ArticleTitleUnsteady aerodynamic and aeroelastic calculations for wings using Euler equations AIAA J. 28 461–469
L. Librescu S. Na (2001) ArticleTitleActive vibration control of doubly tapered thin walled beams using piezoelectric actuation Thin Walled Struct. 39 65–82 Occurrence Handle10.1016/S0263-8231(00)00054-9
Librescu, L., Na, S. S., Kim, S.: Comparative study on vibration control methodologies applied to adaptive anisotropic cantilevers. AIAA 2002-1539. In: Proc. 43rd AIAA/ASME/ASCE/ASC Structures, Structural Dynamics and Materials Conf., Denver, CO, 2002
S. S. Na L. Librescu (1998) ArticleTitleOscillation control of cantilevers via smart materials technology and optimal feedback control: actuator location and power consumption issues J. Smart Mater Struct. 7 833–842 Occurrence Handle10.1088/0964-1726/7/6/011
I. Chopra (2002) ArticleTitleReview of state of art of smart structures and integrated systems AIAA J. 40 2145–2187
E. F. Crawley (1994) ArticleTitleIntelligent structures for aerospace: a technology overview and assessment AIAA J. 31 1689–1699
E. F. Crawley T. DeLuis (1988) ArticleTitleUse of piezoelectric actuators as elements of intelligent structures AIAA J. 25 1373–1385
H. S. Tzou G. L. Anderson (Eds) (1992) Intelligent structural systems Kluwer Norwell, MA
H. S. Tzou (1993) Piezoelectric shells – distributed sensing and control of continuum Kluwer Dordrecht
A. Kugi K. Schlacher H. Irschik (1999) ArticleTitleInfinite dimensional control of nonlinear beam vibrations by piezoelectric actuator and sensor layers Nonlinear Dyn. 19 71–91 Occurrence Handle10.1023/A:1008393904114
H. Irschik M. Krommer U. Pichler (2003) ArticleTitleDynamic shape control of beam type structures by piezoelectric actuation and sensing Int. J. Appl. Electromag. Mech. 17 251–258
J. C. Doyle G. Stein (1981) ArticleTitleMultivariable feedback design: concepts for a classical/modern synthesis IEEE Trans. Automatic Control 26 4–16 Occurrence Handle10.1109/TAC.1981.1102555
M. G. Safonov A. J. Laub G. L. Hartmann (1981) ArticleTitleFeedback properties of multivariable systems: the role and use of the return difference matrix IEEE Trans. Automatic Control 26 47–65 Occurrence Handle10.1109/TAC.1981.1102566
N. A. Lehtomaki N. S. Sandell SuffixJr. M. Athans (1981) ArticleTitleRobustness results in linear quadratic Gaussian based multivariable control designs IEEE Trans. Automatic Control 26 75–92 Occurrence Handle10.1109/TAC.1981.1102565
M. J. Balas (1978) ArticleTitleFeedback control of flexible systems IEEE Trans. Automatic Control 23 673–679 Occurrence Handle10.1109/TAC.1978.1101798
Edwards, C., Spurgeon, S.: Sliding mode control: theory and applications. Taylor & Francis 1998.
M. H. Kim D. J. Inman (2001) ArticleTitleReduction of observation spillover in vibration suppression using a sliding mode observer J. Vibr. Contr. 7 1087–1105
Na, S. S., Librescu, L., Marzocca, P., Kim, M.-H., Jeong, I.-J., Chung, C.: Aeroelastic response of flapped wing systems using robust estimation control methodology. J. Guidance Control Dyn. (in press)
H. Y. Hu E. H. Dowell L. N. Virgin (1998) ArticleTitleStability estimation of high dimensional vibrating systems under state delay feedback control J. Sound Vibr. 214 497–511 Occurrence Handle10.1006/jsvi.1998.1548 Occurrence HandleMR1634007
P. Yu (2003) Bifurcation dynamics in control systems R. Chen D. J. Hill X. Yu (Eds) Bifurcation control, theory and applications Springer Berlin 99–126
M. Basso A. Evangelisti R. Genesio A. Tesi (1998) ArticleTitleOn bifurcation control in time-delay feedback systems J. Bifurcation Chaos 8 713–721 Occurrence Handle10.1142/S0218127498000504
J. Blair S. A. Campbell (1994) ArticleTitleStability and bifurcations of equilibria in a multiple-delayed differential equation SIAM J. Appl. Math. 54 1402–1424 Occurrence Handle10.1137/S0036139993248853
G. Gilsinn (2002) ArticleTitleEstimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter Nonlinear Dyn. 30 103–154 Occurrence Handle10.1023/A:1020455821894
K. Gu S. Niculescu (2003) ArticleTitleSurvey on recent results in the stability and control of time-delay systems J. Dyn. Sys. Trans. ASME 125 158–165
S. Phoojaruenchanachai K. Furuta (1992) ArticleTitleMemoryless stabilization of uncertain linear systems including time-varying state delays IEEE Trans. Automatic Control 37 1022–1026 Occurrence Handle10.1109/9.148363
Gu, Y., Geng, C., Qian, J., Wang, L.: Robust H-inf control for linear time-delay system subject to normbounded nonlinear uncertainty. Proc. 1998 American Control Conf., Philadelphia, PA, June 1998, pp. 2417–2420 (1998)
J. C. Shen (1997) ArticleTitleDesigning stabilizing controllers and observers for uncertain linear systems with time-varying delay Automatica 33 331–333 Occurrence Handle10.1016/S0005-1098(96)00176-8
J. H. Su (1994) ArticleTitleFurther result on the robust stability of linear systems with a single time-delay Sys. Control Lett. 23 375–379 Occurrence Handle10.1016/0167-6911(94)90071-X
P. Yu Y. Yuan J. Xu (2002) ArticleTitleStudy of double Hopf bifurcation and chaos for an oscillator with timedelayed feedback Comm. Nonlinear Sci. Num. Simul. 7 69–91 Occurrence Handle10.1016/S1007-5704(02)00007-2
S. J. Niculescu (2001) Delay effects on stability, a robust control approach. Lecture Notes in Control and Information Sciences 269 Springer London
E. Ott C. Grebogi J. A. Yorke (1990) ArticleTitleControlling chaos Phys. Rev. Lett. 64 1196–1199 Occurrence Handle10.1103/PhysRevLett.64.1196 Occurrence Handle10041332
K. Pyragas (1992) ArticleTitleContinuous control of chaos by self-controlling feedback Phys. Lett. A 170 421–428 Occurrence Handle10.1016/0375-9601(92)90745-8
A. D. Myshkis (1951) ArticleTitleGeneral theory of differential equations with delay Am. Math. Soc. Transl. 55 1–62
L. S. Pontryagin (1955) ArticleTitleOn the zeros of some elementary transcendental functions Am. Math. Soc Transl. 2 95–110
Górecki, H., Popek, L.: Control of the systems with time-delay. IFAC 3rd Symp. on Control of Distributed Parameter Systems, Toulouse, France, 1982
Kolmanovskii, V. B., Nosov, V. R.: Stability of functional differential equations. Mathematics in Science and Engineering, vol. 180. Academic Press, London 1986
Stépán, G.: Retarded dynamical systems: stability and characteristic functions. Pitman Research Notes in Mathematics Series 210. Longman Scientific and Technical, co-published in the USA. Wiley, New York 1989.
Marshall, J. E., Görecki Walton, K., Korytowski, A.: Time-delay systems, stability and performance criteria with applications. In Bell GM. (ed) Series in Mathematics and its Applications. Chichester: Ellis Horwood 1992
N. Olgac B. T. Holm-Hansen (1994) ArticleTitleA novel active vibration absorption technique: delayed resonator J. Sound Vibr. 176 93–104 Occurrence Handle10.1006/jsvi.1994.1360
W. Just T. Bernard M. Ostheimer E. Reibold H. Benner (1997) ArticleTitleOn the mechanism of time-delayed feedback control Phys. Rev. Lett. 78 203–206 Occurrence Handle10.1103/PhysRevLett.78.203
H. Y. Hu Z. H. Wang (1998) ArticleTitleStability analysis of damped SDOF systems with two time-delays in state feedback J. Sound Vibr. 214 213–225 Occurrence Handle10.1006/jsvi.1997.1499 Occurrence HandleMR1632242
Liapunov, A. M.: General theory of the stability of motion. Moskva: Izd., (1950), (English translation: New York: Academic Press 1966)
N. N. Bautin (1984) The behavior of dynamical systems near the boundaries of the domain of stability (in Russian) EditionNumber2 Nauka Moskva
Mei, C., Abdel-Motagaly, K., Chen, R.: Review of nonlinear panel flutter at supersonic and hypersonic speed. CEAS/AIAA/ICASE/NASA Langley Int. Forum on Aeroelasticity and Structural Dynamics, NASA CP-1999-209136/PT 1 (Whitlow, W. Jr., Todd E.N., eds.), pp 171–188 (1999).
C. Mei K. Abdel-Motagaly R. Chen (1999) ArticleTitleReview of nonlinear panel flutter at supersonic and hypersonic speeds Appl. Mech. Rev. 52 321–332
Bismarck-Nasr, M.N.: Structural dynamics in aeronautical engineering. (Przemieniechi J.S., ed.), pp. 229–289. AIAA Education Series; Reston, VA: AIAA, 1999.
G. Cheng C. Mei (2004) ArticleTitleFinite element modal formulation for hypersonic panel flutter analysis with thermal effects AIAA J. 42 687–695
Dowell, E. H., Ilgamov, M.: Studies in nonlinear aeroelasticity, pp. 29–63; 206–277. New York: Springer 1988
D. H. Kim I. Lee (2000) ArticleTitleTransonic and low-supersonic aeroelastic analysis of two degree of freedom airfoil with freeplay nonlinearity J. Sound Vibr. 234 859–880 Occurrence Handle10.1006/jsvi.2000.2907
V. Volterra (1959) Theory of functionals and of integral and integro-differential equations Dover New York
Rugh, W.J.: Nonlinear systems theory, the Volterra-Wiener approach. The Johns Hopkins University Press 1981.
K. Worden G. R. Tomlinson (2001) Nonlinearity in structural dynamics detection, identification and modeling Institute of Physics Publishing Bristol
Dugundji, J. Experimental studies in aeroelasticity of unswept and forward swept graphite/ epoxy wings. In: Proc. Raymond L. Bisplinghoff Memorial Symp., pp. 149–160. Gainesville, FL: University of Florida Press 1986
Weisshaar, T. A.: Aeroelastic tailoring of forward swept wings. J. Aircraft 18, 669–676 (1981); also: Aeroelastic tailoring for unconventional aircraft configurations. Proc. CEAS Int. Forum on Aeroelasticity and Structural Dynamics 1, 89–102 (2001), and Proc. Raymond L. Bisplinghoff Memorial Symp. (Hajela P, eds.), pp. 336–352. Gainesville, FL: University of Florida Press 1986
Weisshaar, T. A.: Aeroelastic tailoring – creative use of unusual materials. AIAA Paper 87 0976. In: Proc. 28th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conf., April 1987
L. Librescu J. Simovich (1988) ArticleTitleGeneral formulation for the aeroelastic divergence of composite swept-forward wing structures J. Aircraft 25 364–371
L. Librescu A. A. Khdeir (1988) ArticleTitleAeroelastic divergence of swept-forward composite wings including warping restraint effect AIAA J. 26 1373–1377
L. Librescu S. Thangjitham (1991) ArticleTitleAnalytical studies on static aeroelastic behavior of forward swept composite wing structures J. Aircraft 28 151–157
L. Librescu P. Marzocca W. A. Silva (2004) ArticleTitleLinear/nonlinear supersonic panel flutter in a hightemperature field J. Aircraft 41 918–924
Librescu, L., Marzocca, P., Silva, W. A.: Linear/nonlinear aeroelastic behavior of thermally damaged flat panels in a supersonic flow field. In: 5th Int. Congress of Thermal Stresses and Related Topics, TS2003, Virginia Polytechnic Institute and State University, Blacksburg, VA, June 8–11, 2003.
Librescu, L., Marzocca, P.: Flutter and postflutter active control of thermally degraded panels in a high supersonic flowfield. In: 6th Int. Congress of Thermal Stresses and Related Topics, TS2005, Vienna, Austria, May 26–29, 2005.
D. D. Liu Z. X. Yao D. Sarhaddi F. R. Chavez (1997) ArticleTitleFrom piston theory to a unified hypersonic– supersonic lifting surface method J. Aircraft 34 304–312
Polli, G. M., Librescu, L., Mastroddi, F.: Aerothermoelastic response of composite aircraft swept wings impacted by a laser beam. In: 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., April 19–22, 2004. AIAA-2004-2046.
E. H. Dowell D. M. Tang (2002) ArticleTitleNonlinear aeroelasticity and unsteady aerodynamics AIAA J. 40 1697–1707
H. Irschik K. Schlacher (Eds) (2004) Advanced dynamics and control of structures and machines CISM Courses and Lectures, vol. 444 International Center for Mechanical Sciences Springer Wien New York
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This paper represents an updated version of the General Lecture presented at the 3rd European Conference on Structural Control, July 12–15, 2004, Vienna, Austria.
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Librescu, L., Marzocca, P. Advances in the linear/nonlinear control of aeroelastic structural systems. Acta Mechanica 178, 147–186 (2005). https://doi.org/10.1007/s00707-005-0222-6
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DOI: https://doi.org/10.1007/s00707-005-0222-6