multimodal broadband; targeted energy transfers; multi-degree-of-freedom; nonlinear energy sinks; aeroelastic instability suppression; structural nonlinearities
Abstract :
[en] In this last of a three paper sequence, we use simultaneous multimodal broadband targeted energy transfers to multi-degree-of-freedom nonlinear energy sinks to improve the robustness of aeroelastic instability suppression of a rigid wing with structural nonlinearities. A numerical bifurcation analysis of limit cycle oscillations of the wing with the multi-degree-of-freedom nonlinear energy sinks attached shows that controlling the lower parameter value for limit point cycle bifurcation to occur above Hopf bifurcation is crucial to enhancing the robustness of limit cycle oscillation suppression. We demonstrate that multi-degree-of-freedom nonlinear energy sinks can greatly enhance the robustness of limit cycle oscillation suppression, compared with single-degree-of-freedom nonlinear energy sinks (which were studied in our previous papers), with a much smaller total mass.We also investigate the nonlinear modal interactions that occur between the aeroelastic modes and the multi-degree-of-freedom nonlinear energy sinks, in an effort to gain a physical understanding of the mechanisms governing instability suppression. We demonstrate that a properly designed multi-degree-of-freedom nonlinear energy sink provides robustness of aeroelastic instability suppression by efficiently, passively, and rapidly transferring a significant portion of unwanted vibration energy to the furthest mass of the nonlinear energy sink. Consideration of other types of multi-degree-of-freedom nonlinear energy sinks suggests that the robustness enhancement is achieved by the concentrated mass effect of the attached nonlinear energy sinks.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others Mechanical engineering
Author, co-author :
Lee, Young S.; University of Illinois at Urbana Champaign, Urbana, Illinois, 61801
Vakakis, Alexander F.; National Technical University of Athens,Greece > Department of Applied Mathematical and Physical Sciences
Bergman, Lawrence A.; University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
McFarland, D. Michael; University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Language :
English
Title :
Enhancing robustness of aerolastic instability suppression using MDOF energy sinks
Publication date :
2008
Journal title :
AIAA Journal
ISSN :
0001-1452
eISSN :
1533-385X
Publisher :
American Institute of Aeronautics and Astronautics, Reston, United States - Virginia
Lee, Y., Vakakis, A., Bergman, L., McFarland, D. M., and Kerschen, G., "Suppressing Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory," AIAA Journal, Vol. 45, No. 3, March 2007, pp. 693-711. doi:10.2514/1.24062
Lee, Y., Kerschen, G., McFarland, D. M., Hill, W., Nichkawde, C., Strganac, T., Bergman, L., and Vakakis, A., "Suppressing Aeroelasdc Instability Using Broadband Passive Targeted Energy Transfers, Part 2: Experiments," AIAA Journal, Vol. 45, No. 10, Oct. 2007, pp. 2391-2400. doi: 10.2514/1.28300
Panagopoulos, P. N., Vakakis, A. F., and Tsakirtzis, S., "Transient Resonant Interactions of Finite Linear Chains with Essentially Nonlinear End Attachments Leading to Passive Energy Pumping," International Journal of Solids and Structures, Vol. 41, Nos. 22-23, Nov. 2004, pp. 6505-6528. doi:10.1016/j.ijsolstr.2004.05.005
Tsakirtzis, S., Panagopoulos, P., Kerschen, G., Gendelman, O., Vakakis, A., and Bergman, L., "Complex Dynamics and Targeted Energy Transfer in Linear Oscillators Coupled to Multi-Degree-of-Freedom Essentially Nonlinear Attachments," Nonlinear Dynamics, Vol. 48, No. 3, May 2007, pp. 285-318. doi:10.1007/s11071-006-9089-x
Dhooge, A., Govaerts, W., and Kuznetsov, Y., "MATCONT: A Matlab Package for Numerical Bifurcation Analysis of ODEs," ACM Transactions on Mathematical Software, Vol. 29, No. 2, 2003, pp. 141-164. doi:10.1145/779359.779362
Lee, Y., Vakakis, A., Bergman, L., McFarland, D. M., and Kerschen, G., "Triggering Mechanisms of Limit Cycle Oscillations in a Two-Degree-of-Freedom Wing Flutter Model," Journal of Fluids and Structures, Vol. 21, Nos. 5-7, 2005, pp. 485-529. doi: 10.1016/j. jfluidstructs.2005.08.01
Kuznetsov, Y., Elements of Applied Bifurcation Theory, Springer-Verlag, New York, 1995.
Arnold, V., Dynamical Systems III (Encyclopaedia of Mathematical Sciences), Springer-Verlag, Berlin/Heidelberg, Germany, 1988.
Vakakis, A., and Gendelman, O., "Energy Pumping in Coupled Mechanical Oscillators, Part 2: Resonance Capture," Journal of Applied Mechanics, Vol. 68, No. 1, Jan. 2001, pp. 42-48. doi:10.1115/1.1345525
Zuo, L., and Nayfeh, S., "Minimas Optimization of Multi-Degree-of-Freedom Tuned-Mass Dampers." Journal of Sound and Vibration, Vol. 272, Nos. 3-5, 2004, pp. 893-908. doi:10.1016/S002-460X(03) 005500-5
Zuo, L., and Nayfeh, S., 'The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation," Journal of Vibration and Acoustics, Vol. 128, No. 1, Feb. 2006, pp. 56-65. doi:10.1115/1.2128639