Advances in aircraft and spacecraft science

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Aircraft wings dynamics suppression by optimal NESs designed through an Efficient stochastic linearisation approach

  • Navarra, Giacomo (Faculty of Engineering and Architecture, Kore University of Enna, Cittadella Universitaria) ;
  • Iacono, Francesco Lo (Faculty of Engineering and Architecture, Kore University of Enna, Cittadella Universitaria) ;
  • Oliva, Maria (Faculty of Engineering and Architecture, Kore University of Enna, Cittadella Universitaria) ;
  • Esposito, Antonio (Faculty of Engineering and Architecture, Kore University of Enna, Cittadella Universitaria)
  • Received : 2019.12.31
  • Accepted : 2020.05.18
  • Published : 2020.09.25
⟨ Previous Next ⟩

Abstract

Non-linear energy sink (NES) is an emerging passive absorber able to mitigate the dynamic response of structures without any external energy supply, resonating with all the modes of the primary structure to control. However, its inherent non-linearities hinder its large-scale use and leads to complicated design procedures. For this purpose, an approximate design approach is herein proposed in a stochastic framework. Since loads are random in nature, the stochastic analysis of non-linear systems may be performed by means of computational intensive techniques such as Monte Carlo simulations (MCS). Alternatively, the Stochastic Linearisation (SL) technique has proven to be an effective tool to investigate the performance of different passive control systems under random loads. Since controlled systems are generally non-classically damped and most of SL algorithms operate recursively, the computational burden required is still large for those problems that make intensive use of SL technique, as optimal design procedures. Herein, a procedure to speed up the Stochastic Linearisation technique is proposed by avoiding or strongly reducing numerical evaluations of response statistics. The ability of the proposed procedure to effectively reduce the computational effort and to reliably design the NES is showed through an application on a well-known case study related to the vibrations mitigation of an aircraft wing.

Keywords

References

  1. Artale, V., Navarra, G., Ricciardello, A. and Barone, G. (2017), "Exact closed-form fractional spectral moments for linear fractional oscillators excited by a white noise", ASCE-ASME J Risk Uncertainty, Part B, 3(3), https://doi.org/10.1115/1.4036700.
  2. Atalik, T.S. and Utku, S. (1976), "Stochastic Linearization of Multi-Degree-of-Freedom Nonlinear System", Earthq. Eng. Struct. D., 4(March 1975), 411-420, https://doi.org/10.1002/eqe.4290040408.
  3. Barone, G., Lo Iacono, F., Navarra, G. and Palmeri, A. (2019), "Closed-form stochastic response of linear building structures to spectrum-consistent seismic excitations", Soil Dyn. Earthq. Eng., 125, 105724, https://doi.org/10.1016/j.soildyn.2019.105724.
  4. Bergeot, B., Bellizzi, S. and Cochelin, B. (2016), "Passive suppression of helicopter ground resonance instability by means of a strongly nonlinear absorber", Adv. Aircraft Spacecraft Sci., 3(3), 271-298, https://doi.org/10.12989/aas.2016.3.3.271.
  5. Der Kiureghian, A. (1980), "Structural response to stationary excitation", J. Eng. Mech. -ASCE, 106(6), 1195-1213.
  6. Di Matteo, A., Lo Iacono, F., Navarra, G. and Pirrotta, A. (2014), "Direct evaluation of the equivalent linear damping for TLCD systems in random vibration for pre-design purposes", Int. J. Nonlinear Mech., 63, 19-30, https://doi.org/10.1016/j.ijnonlinmec.2014.03.009.
  7. Di Paola, M. and Muscolino, G. (1986), "On the convergent parts of high order structural responses", J. Sound Vib., 110, 233-245, https://doi.org/10.1016/S0022-460X(86)80207-3.
  8. Di Paola, M. and Muscolino, G. (1988), "Analytic evaluation of spectral moments", J. Sound Vib., 124(3), 479-488, https://doi.org/10.1016/S0022-460X(88)81389-0.
  9. Di Paola, M. and Navarra, G. (2009), "Stochastic seismic analysis of MDOF structures with nonlinear viscous dampers", Struct. Control Hlth., 16(3), 303-318, https://doi.org/10.1002/stc.254.
  10. Elishakoff, I. (2000), "Stochastic linearization technique: a new interpretation and a selective review", Shock Vib., 32, 179-188, https://doi.org/10.1177/058310240003200301.
  11. Gendelman, O. (2001), "Transition of Energy to a Nonlinear Localized Mode in a Highly Asymmetric System of Two Oscillators", Nonlinear Dynam., 25(1/3), 237-253, https://doi.org/10.1023/A:1012967003477.
  12. Gendelman, O., Manevitch, L., Vakakis, A. and M'Closkey, R. (2001), "Energy Pumping in Nonlinear Mechanical Oscillators: Part I - Dynamics of the Underlying Hamiltonian Systems", J. Appl. Mech., 68(1), 34, https://doi.org/10.1115/1.1345524.
  13. Gendelman, O.V. (2008), "Targeted energy transfer in systems with non-polynomial nonlinearity", J. Sound Vib., 315(3), 732-745, https://doi.org/10.1016/j.jsv.2007.12.024.
  14. Gendelman, O.V., Sapsis, T., Vakakis, A.F. and Bergman, L.A. (2011), "Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators", J. Sound Vib., 330(1), 1-8, https://doi.org/10.1016/j.jsv.2010.08.014.
  15. Gendelman, O.V., Sigalov, G., Manevitch, L.I., Mane, M., Vakakis, A.F. and Bergman, L.A. (2012), "Dynamics of an Eccentric Rotational Nonlinear Energy Sink", J. Appl. Mech., 79(1), 011012, https://doi.org/10.1115/1.4005402.
  16. Gourdon, E., Alexander, N., Taylor, C., Lamarque, C. and Pernot, S. (2007), "Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results", J. Sound Vib., 300(3-5), 522-551, https://doi.org/10.1016/j.jsv.2006.06.074.
  17. Guo, A., Xu, X.L. and Wu, B. (2002), "Seismic reliability analysis of hysteretic structure with viscoelastic dampers", Eng. Struct., 24, 373-383, https://doi.org/10.1016/S0141-0296(01)00103-1.
  18. Hubbard, S.A., McFarland, D.M., Bergman, L.A. and Vakakis, A.F. (2010), "Targeted Energy Transfer Between a Model Flexible Wing and Nonlinear Energy Sink", J. Aircraft, 47(6), 1918-1931, https://doi.org/10.2514/1.C001012.
  19. Igusa, T., Der Kiureghian, A. and Sackman, J.L. (1984), "Modal decomposition method for stationary response of non-classically damped systems", Earthq. Eng. Struct. D., 12(1), 121-136, https://doi.org/10.1002/eqe.4290120109.
  20. Kerschen, G., Lee, Y., Vakakis, A., McFarland, D. and Bergman, L. (2005), "Irreversible Passive Energy Transfer in Coupled Oscillators with Essential Nonlinearity", SIAM J. Appl. Math., 66(2), 648-679, https://doi.org/10.1137/040613706.
  21. Kerschen, G., McFarland, D., Kowtko, J., Lee, Y., Bergman, L. and Vakakis, A. (2007), "Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity", J. Sound Vib., 299(4), 822-838, https://doi.org/10.1016/j.jsv.2006.07.029.
  22. Lagarias, J., Reeds, J., Wright, M. and Wright, P. (1998), "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions", SIAM J. Optimiz., 9(1), 112-147, https://doi.org/10.1137/S1052623496303470.
  23. Lee, Y., Kerschen, G., McFarland, D., Hill, W., Nichkawde, C., Strganac, T., Bergman, L. and Vakakis, A. (2007a), "Suppressing Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 2: Experiments", AIAA J., 45(10), 2391-2400, https://doi.org/10.2514/1.28300.
  24. Lee, Y., Kerschen, G., Vakakis, A., Panagopoulos, P., Bergman, L. and McFarland, D. (2005), "Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment", Physica D, 204(1-2), 41-69, https://doi.org/10.1016/j.physd.2005.03.014.
  25. Lee, Y., Vakakis, A., Bergman, L., McFarland, D. and Kerschen, G. (2007b), "Suppression Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory", AIAA J., 45(3), 693-711, https://doi.org/10.2514/1.24062.
  26. Lee, Y., Vakakis, A., Bergman, L., McFarland, D., Kerschen, G., Nucera, F., Tsakirtzis, S. and Panagopoulos, P. (2008a), "Passive non-linear targeted energy transfer and its applications to vibration absorption: a review", in "Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics", volume 222, pages 77-134, https://doi.org/10.1243/14644193JMBD118.
  27. Lee, Y.S., Vakakis, a.F., Bergman, L.a., McFarland, D.M. and Kerschen, G. (2008b), "Enhancing the Robustness of Aeroelastic Instability Suppression Using Multi-Degree-of-Freedom Nonlinear Energy Sinks", AIAA J., 46(6), 1371-1394, https://doi.org/10.2514/1.30302.
  28. Lee, Y.S., Vakakis, A.F., Bergman, L.A. and Michael McFarland, D. (2006), "Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non-linear energy sinks", Struct. Control Hlth., 13(1), 41-75, https://doi.org/10.1002/stc.143.
  29. McFarland, D., Bergman, L. and Vakakis, A. (2005), "Experimental study of non-linear energy pumping occurring at a single fast frequency", Int. J. Nonlinear Mech., 40(6), 891-899, https://doi.org/10.1016/j.ijnonlinmec.2004.11.001.
  30. Navarra, G., Lo Iacono, F. and Oliva, M. (2020a), "An Efficient Stochastic Linearisation Procedure for the Seismic Optimal Design of Passive Control Devices", Front. Built Env., 6, 32, URL https://www.frontiersin.org/article/10.3389/fbuil.2020.00032, https://doi.org/10.3389/fbuil.2020.00032.
  31. Navarra, G., Lo Iacono, F., Oliva, M. and Cascone, D. (2020b), "Speeding up the stochastic linearisation for systems controlled by non-linear passive devices", Lecture Notes in Mechanical Engineering, pages 1625-1644, conference of 24th Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2019 ; Conference Date: 15 September 2019 Through 19 September 2019; Conference Code:238859, https://doi.org/10.1007/978-3-030-41057-5 131.
  32. Nguyen, T.A. and Pernot, S. (2012), "Design criteria for optimally tuned nonlinear energy sinkspart 1: transient regime", Nonlinear D., 69(1-2), 1-19, https://doi.org/10.1007/s11071-011-0242-9.
  33. Nucera, F., Lo Iacono, F., McFarland, D., Bergman, L. and Vakakis, A. (2008), "Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame: Experimental results", Journal of Sound and Vibration, 313(1-2), 57-76, https://doi.org/10.1016/j.jsv.2007.11.018.
  34. Nucera, F., Vakakis, A., McFarland, D., Bergman, L. and Kerschen, G. (2007), "Targeted energy transfers in vibro-impact oscillators for seismic mitigation", Nonlinear D., 50(3), 651-677, https://doi.org/10.1007/s11071-006-9189-7.
  35. Oliva, M., Barone, G. and Navarra, G. (2017), "Optimal design of Nonlinear Energy Sinks for SDOF structures subjected to white noise base excitations", Eng. Struct., 145, 135-152, https://doi.org/10.1016/j.engstruct.2017.03.027.
  36. Roberts, J.B. and Spanos, P.D. (2003), Random vibration and statistical linearization, Dover, Mineola, NY, USA.
  37. Sapsis, T.P., Dane Quinn, D., Vakakis, A.F. and Bergman, L.a. (2012), "Effective Stiffening and Damping Enhancement of Structures With Strongly Nonlinear Local Attachments", J. Vib. Acoust., 134(1), 011016, https://doi.org/10.1115/1.4005005.
  38. Sigalov, G., Gendelman, O.V., AL-Shudeifat, M.A., Manevitch, L.I., Vakakis, A.F. and Bergman, L.A. (2012), "Resonance captures and targeted energy transfers in an inertially-coupled rotational nonlinear energy sink", Nonlinear D., 69(4), 1693-1704, https://doi.org/10.1007/s11071-012-0379-1.
  39. Socha, L. (2005), "Linearization in Analysis of Nonlinear Stochastic Systems: Recent ResultsPart I: Theory", Appl. Mech. Rev., 58(3), 178, https://doi.org/10.1115/1.1896368.
  40. Starosvetsky, Y. and Gendelman, O. (2008), "Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber", Nonlinear D., 51(1-2), 47, https://doi.org/10.1007/s11071-006-9168-z.
  41. Vakakis, A., Gendelman, O., Bergman, L., McFarland, D., Kerschen, G. and Lee, Y. (2009), Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, volume 156 of Solid Mechanics and Its Applications, Springer Netherlands, https://doi.org/10.1007/978-1-4020-9130-8.
  42. Vakakis, A.F. (2001), "Inducing Passive Nonlinear Energy Sinks in Vibrating Systems", J Vib.Acoust., 123(3), 324, https://doi.org/10.1115/1.1368883.
  43. Vanmarcke, E.H. (1972), "Properties of spectral moments with applications to random vibration", J. Eng. Mech. ASCE, 98(2), 425-446.
  44. Vanmarcke, E.H. (1975), "On the Distribution of the First-Passage Time for Normal Stationary Random Processes", J. Appl. Mech., 42(1), 215, https://doi.org/10.1115/1.3423521.
  45. Wang, J., Wierschem, N., Spencer, B. and Lu, X. (2015a), "Experimental study of track nonlinear energy sinks for dynamic response reduction", Eng. Struct., 94, 9-15, https://doi.org/10.1016/j.engstruct.2015.03.007.
  46. Wang, J., Wierschem, N., Spencer, B. and Lu, X. (2015b), "Track Nonlinear Energy Sink for Rapid Response Reduction in Building Structures", J. Eng. Mech. ASCE, 141(1), 04014104, https://doi.org/10.1061/(ASCE)EM.1943-7889.0000824.