×

Control of limit cycle oscillations of a two-dimensional aeroelastic system. (English) Zbl 1191.74013

Summary: Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO). It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be efficiently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] E. H. Dowell and D. Tang, “Nonlinear aeroelasticity and unsteady aerodynamics,” AIAA Journal, vol. 40, no. 9, pp. 1697-1707, 2002. · doi:10.2514/2.1853
[2] A. Raghothama and S. Narayanan, “Non-linear dynamics of a two-dimensional air foil by incremental harmonic balance method,” Journal of Sound and Vibration, vol. 226, no. 3, pp. 493-517, 1999. · doi:10.1006/jsvi.1999.2260
[3] L. Liu, Y. S. Wong, and B. H. K. Lee, “Application of the centre manifold theory in non-linear aeroelasticity,” Journal of Sound and Vibration, vol. 234, no. 4, pp. 641-659, 2000. · Zbl 1237.74077 · doi:10.1006/jsvi.1999.2895
[4] H. C. Gilliatt, T. W. Strganac, and A. J. Kurdila, “An investigation of internal resonance in aeroelastic systems,” Nonlinear Dynamics, vol. 31, no. 1, pp. 1-22, 2003. · Zbl 1026.70023 · doi:10.1023/A:1022174909705
[5] B. H. K. Lee, L. Y. Jiang, and Y. S. Wong, “Flutter of an airfoil with a cubic restoring force,” Journal of Fluids and Structures, vol. 13, no. 1, pp. 75-101, 1999. · doi:10.1006/jfls.1998.0190
[6] C. C. Chabalko, M. R. Hajj, D. T. Mook, and W. A. Silva, “Characterization of the LCO response behaviors of the NATA model,” in Proceedings of the 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol. 5, pp. 3196-3206, Newport, RI, USA, May 2006, AIAA paper no.2006-1852.
[7] E. H. Abed and J.-H. Fu, “Local feedback stabilization and bifurcation control. I. Hopf bifurcation,” Systems & Control Letters, vol. 7, no. 1, pp. 11-17, 1986. · Zbl 0587.93049 · doi:10.1016/0167-6911(86)90095-2
[8] E. H. Abed and J.-H. Fu, “Local feedback stabilization and bifurcation control. II. Stationary bifurcation,” Systems & Control Letters, vol. 8, no. 5, pp. 467-473, 1987. · Zbl 0626.93058 · doi:10.1016/0167-6911(87)90089-2
[9] T. W. Strganac, J. Ko, D. E. Thompson, and A. J. Kurdila, “Identification and control of limit cycle oscillations in aeroelastic systems,” in Proceedings of the 40th AIAA/ASME/ASCE/AHS/ASC Structrures, Structural Dynamics, and Materials Conference and Exhibit, vol. 3, pp. 2173-2183, St. Louis, Mo, USA, April 1999, AIAA paper no. 99-1463.
[10] L. Librescu, S. Na, P. Marzocca, C. Chung, and M. K. Kwak, “Active aeroelastic control of 2-D wing-flap systems operating in an incompressible flowfield and impacted by a blast pulse,” Journal of Sound and Vibration, vol. 283, no. 3-5, pp. 685-706, 2005. · doi:10.1016/j.jsv.2004.05.010
[11] W. Kang, “Bifurcation control via state feedback for systems with a single uncontrollable mode,” SIAM Journal on Control and Optimization, vol. 38, no. 5, pp. 1428-1452, 2000. · Zbl 0968.93035 · doi:10.1137/S0363012997325927
[12] A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics. Analytical, Computational, and Experimental Methods, Wiley Series in Nonlinear Science, John Wiley & Sons, New York, NY, USA, 1995. · Zbl 0848.34001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.