Structural Engineering and Mechanics

  • 제28권1호
  • /
  • Pages.107-127
  • /
  • 2008
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

On the nonlinear structural analysis of wind turbine blades using reduced degree-of-freedom models

  • Holm-Jorgensen, K. (Department of Civil Engineering, Aalborg University) ;
  • Staerdahl, J.W. (Department of Civil Engineering, Aalborg University) ;
  • Nielsen, S.R.K. (Department of Civil Engineering, Aalborg University)
  • 투고 : 2006.10.04
  • 심사 : 2007.08.17
  • 발행 : 2008.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

Wind turbine blades are increasing in magnitude without a proportional increase of stiffness for which reason geometrical and inertial nonlinearities become increasingly important. Often these effects are analysed using a nonlinear truncated expansion in undamped fixed base mode shapes of a blade, modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response and stability conditions. It is demonstrated that the response predicted by such models in some cases becomes instable or chaotic. However, as a consequence of the energy flow the stability is increased and the tendency of chaotic vibrations is reduced as the number of modes are increased. The FE model representing the case of infinitely many included modes, is shown to predict stable and ordered response for all considered parameters. Further, the analysis shows that the reduced-degree-of-freedom model of relatively low order overestimates the response near resonance peaks, which is a consequence of the small number of included modes. The qualitative erratic response and stability prediction of the reduced order models take place at frequencies slightly above normal operation. However, for normal operation of the wind turbine without resonance excitation 4 modes in the reduced-degree-of-freedom model perform acceptable.

키워드

참고문헌

  1. Apiwattanalunggarn, P., Shaw, S.W., Pierre, C. and Jiang, D. (2003), "Finite-element-based nonlinear modal reduction of a rotation beam with large-amplitude motion", J. Vib. Control, 9, 235-263 https://doi.org/10.1177/107754603030749
  2. Baker, C.P., Genaux, M.E. and Burton, T.D. (1993), "Experimental study of chaos in a flexible parametrically excited beam", Dyn. Vib. Time-Varying Syst. Struct., 56, 195-206
  3. Behdinan, K., Stylianou, M.C. and Tabarrok, B. (1998), "Co-rotational dynamic analysis of flexible beams", Comput. Method. Appl. M., 154, 151-161 https://doi.org/10.1016/S0045-7825(97)00124-2
  4. Crisfield, M.A. (1990), "A consistent co-rotational formulation for non-linear, three-dimensional, beamelements", Comput. Method. Appl. M., 81, 131-150 https://doi.org/10.1016/0045-7825(90)90106-V
  5. Crisfield, M.A., Galvanetto, U. and Jeleni , G. (1997), "Dynamics of 3-D co-rotational beams", Comput. Mech., 20, 507-519 https://doi.org/10.1007/s004660050271
  6. Martin O.L. Hansen (2000), Aerodynamics of Wind Turbines, James & James (Science Publishers) Ltd
  7. Steen Krenk (2005), "Non-linear modelling and analysis of structures and solids", Lecture notes. Department of Mechanical Engineering, Technical University of Denmark
  8. Larsen, J.W. and Nielsen, S.R.K. (2006a), "Non-linear dynamics of wind turbine wings", J. Non-Linear Mech., 41, 629-643 https://doi.org/10.1016/j.ijnonlinmec.2006.01.003
  9. Larsen, J.W. and Nielsen, S.R.K. (2006b), "Nonlinear parametric instability of wind turbine wings", J. Sound Vib., (in press.)
  10. Hsiao, K.M., Lin, J.Y. and Lin, W.Y. (1999), "A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams", Comput. Method. Appl. M., 169, 1-18 https://doi.org/10.1016/S0045-7825(98)00152-2
  11. Nayfeh, A.H., Chin, C. and Nayfeh, S.A. (1995), "Nonlinear normal modes of a cantilever beam", J. Vib. Acoustics, 117, 417-481
  12. Sandhu, J.S., Stevens, K.A. and Davies, G.A.O. (1990), "A 3-D, co-rotational, curved and twisted beam element", Comput. Struct., 35(1), 69-79 https://doi.org/10.1016/0045-7949(90)90257-3
  13. Volovoi, V.V., Hodges, D.H., Cesnik, C.E.S. and Popescu, B. (2001), "Assessment of beam modeling methods for rotor blade applications", Math. Comput. Model., 33, 1099-1112 https://doi.org/10.1016/S0895-7177(00)00302-2
  14. Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A. (1984), "Determining lyapunov exponents from a time series", Physica, 16D, 285-317
  15. Yu, W., Hodges, D.H., Volovoi, V. and Cesnik, C.E.S. (2002), "On timoshenko-like modelling of initially curved and twisted composite beams", J. Solids Struct., 39, 5101-5121 https://doi.org/10.1016/S0020-7683(02)00399-2

피인용 문헌

  1. Wind-induced responses and equivalent static wind loads of tower-blade coupled large wind turbine system vol.52, pp.3, 2014, https://doi.org/10.12989/sem.2014.52.3.485
  2. Non-linear aeroelasticity: An approach to compute the response of three-blade large-scale horizontal-axis wind turbines vol.66, 2014, https://doi.org/10.1016/j.renene.2013.12.040
  3. Active load control for wind turbine blades using trailing edge flap vol.16, pp.3, 2013, https://doi.org/10.12989/was.2013.16.3.263