Nonlinear dynamics of a wind turbine tower

doi:10.1007/s11465-019-0524-3

Front. Mech. Eng.

2019, Vol. 14

Issue (3) : 342-350 https://doi.org/10.1007/s11465-019-0524-3

RESEARCH ARTICLE

Nonlinear dynamics of a wind turbine tower

A. GESUALDO¹, A. IANNUZZO¹, F. PENTA², M. MONACO³(

)

¹. Department of Structures for Engineering and Architecture, University of Naples “Federico II”, 80125 Naples, Italy
². Department of Industrial Engineering, University of Naples “Federico II”, 80125 Naples, Italy
³. Department of Architecture and Industrial Design, University of Campania “Luigi Vanvitelli”, 81031 Aversa (Ce), Italy

Download: PDF(694 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

The recent proliferation of wind turbines has revealed problems in their vulnerability under different site conditions, as evidenced by recent collapses of wind towers after severe actions. Analyses of structures subjected to variable actions can be conducted through several methods with different accuracy levels. Nonlinear dynamics is the most reliable among such methods. This study develops a numerical procedure to obtain approximate solutions for rigid-plastic responses of structures subjected to base harmonic pulses. The procedure’s model is applied to a wind turbine tower subjected to inertial forces generated by harmonic ground acceleration, and failure is assumed to depend on the formation of shear hinges. The proposed approach provides an efficient representation of the post-elastic behavior of the structure, has a low computational cost and high effectiveness, and uses a limited number of mechanical parameters.

Keywords nonlinear dynamics plastic shear failure modal approximation time history

Corresponding Author(s): M. MONACO

Online First Date: 02 November 2018 Issue Date: 24 July 2019

Cite this article:

A. GESUALDO,A. IANNUZZO,F. PENTA, et al. Nonlinear dynamics of a wind turbine tower[J]. Front. Mech. Eng., 2019, 14(3): 342-350.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-019-0524-3
https://academic.hep.com.cn/fme/EN/Y2019/V14/I3/342

Fig.1 Elastic-perfectly plastic body

Fig.2 (a) Wind turbine tower geometry; (b) Rigid-plastic constitutive law; (c) shear strain representation

Fig.3 Time histories of the plastic shear strain rate at the base (left) and at 13 m hinge level (right) for amplitude

a 0 = 0.3 g

(with g gravity acceleration) and

f = ω 2 π = 0.4775

Hz with

ω = 3

s^?²

Fig.4 Time histories of the displacement at the plastic hinge levels (left) and at the top of the tower (right) for amplitude

a 0 = 0.3 g

and

f = ω 2 π = 0.4775

Hz with

ω = 3

s^?²

Fig.5 Variation of the maximum and minimum displacements versus the base motion acceleration’s amplitude corresponding to different frequencies

Fig.6 Variation of the plastic hinge position versus amplitude at two different frequencies

1	B Wen, S Wei, K Wei, et al. Power fluctuation and power loss of wind turbines due to wind shear and tower shadow. Frontiers of Mechanical Engineering, 2017, 12(3): 321–332 https://doi.org/10.1007/s11465-017-0434-1
2	S Chen, Q Li, Y Liu, et al. Dynamic elastoplastic analysis using the meshless local natural neighbor interpolation method. International Journal of Computational Methods, 2011, 8(3): 463–481 https://doi.org/10.1142/S0219876211002629
3	C Bonavolontà, G Peluso, M Valentino, et al. Detection of magnetomechanical effect in structural steel using SQUIDs and flux-gate sensors. Journal of Superconductivity and Novel Magne-tism, 2009, 22(8): 833–839 https://doi.org/10.1007/s10948-009-0507-4
4	R B Schubak, D L Anderson, M D Olson. Simplified dynamic analysis of rigid-plastic beams. International Journal of Impact Engineering, 1989, 8(1): 27–42 https://doi.org/10.1016/0734-743X(89)90029-8
5	A Gesualdo, M Monaco. Constitutive behaviour of quasi-brittle materials with anisotropic friction. Latin American Journal of Solids and Structures, 2015, 12(4): 695–710 https://doi.org/10.1590/1679-78251345
6	M Fraldi, A Gesualdo, F Guarracino. Influence of actual plastic hinge placement on the behavior of ductile frames. Journal of Zhejiang University. Science A, 2014, 15(7): 482–495 https://doi.org/10.1631/jzus.A1400031
7	C Cennamo, A Gesualdo, M Monaco. Shear plastic constitutive behaviour for near-fault ground motion. Journal of Engineering Mechanics, 2017, 143(9): 04017086 https://doi.org/10.1061/(ASCE)EM.1943-7889.0001300
8	C Málaga-Chuquitaype, A Y Elghazouli, R Bento. Rigid-plastic models for the seismic design and assessment of steel framed structures. Earthquake Engineering & Structural Dynamics, 2009, 38(14): 1609–1630 https://doi.org/10.1002/eqe.920
9	T Nonaka. Shear and bending response of a rigid-plastic beam to blast-type loading. Ingenieur-Archiv, 1977, 46(1): 35–52 https://doi.org/10.1007/BF00534958
10	Q M Li, H Meng. Pulse loading shape effects on pressure-impulse diagram of an elastic-plastic, single-degree-of-freedom structural model. International Journal of Mechanical Sciences, 2002, 44(9): 1985–1998 https://doi.org/10.1016/S0020-7403(02)00046-2
11	P S Symonds, W T J Fleming Jr. Parkes revisited: On rigid-plastic and elastic-plastic dynamic structural analysis. International Journal of Impact Engineering, 1984, 2(1): 1–36 https://doi.org/10.1016/0734-743X(84)90013-7
12	M T Liang, B J Lee, S S Yang. On the rigid ideally plastic deformation of cantilever beam subjected to tip impact. Journal of Marine Science and Technology, 1997, 5(1): 39–46
13	D L Smith, C L Sahlit. Dynamic response of pulse loaded structures as a linear complementarity problem. Engineering Optimization, 1991, 18(1–3): 23–41 https://doi.org/10.1080/03052159108941010
14	A Khan, D L Smith, B A Izzuddin. Investigation of rigid-plastic beams subjected to impact using linear complementarity. Engineering Structures, 2013, 50: 137–148 https://doi.org/10.1016/j.engstruct.2012.12.005
15	R Z Wang, K C Tsai, B Z Lin. Extremely large displacement dynamic analysis of elastic-plastic plane frames. Earthquake Engineering & Structural Dynamics, 2011, 40(13): 1515–1533 https://doi.org/10.1002/eqe.1102
16	Q M Li. Continuity conditions at bending and shearing interfaces of rigid, perfectly plastic structural elements. International Journal of Solids and Structures, 2000, 37(27): 3651–3665 https://doi.org/10.1016/S0020-7683(98)00310-2
17	G Chierchiello, A Gesualdo, A Iannuzzo, et al. Structural modeling and conservation of single columns in archaeological areas. In: Proceedings of the XIV International Forum ‘Le vie dei mercanti’. Napoli, 2015, 2012–2020
18	A Gesualdo, A Iannuzzo, F Penta, et al. Homogenization of a Vierendeel girder with elastic joints into an equivalent polar beam. Journal of Mechanics of Materials and Structures, 2017, 12(4): 485–504 https://doi.org/10.2140/jomms.2017.12.485
19	F Penta, M Monaco, G P Pucillo, et al. Periodic beam-like structures homogenization by transfer matrix eigen-analysis: A direct approach. Mechanics Research Communications, 2017, 85: 81–88 https://doi.org/10.1016/j.mechrescom.2017.08.007
20	A Paglietti, M C Porcu. Rigid-plastic approximation to predict plastic motion under strong earthquakes. Earthquake Engineering & Structural Dynamics, 2001, 30(1): 115–126 https://doi.org/10.1002/1096-9845(200101)30:1<115::AID-EQE999>3.0.CO;2-V
21	Y T Ren, X M Qiu, T X Yu. The sensitivity analysis of a geometrically unstable structure under various pulse loading. International Journal of Impact Engineering, 2014, 70: 62–72 https://doi.org/10.1016/j.ijimpeng.2014.03.005
22	M Monaco, M Guadagnuolo, A Gesualdo. The role of friction in the seismic risk mitigation of freestanding art objects. Natural Hazards, 2014, 73(2): 389–402 https://doi.org/10.1007/s11069-014-1076-9
23	A Gesualdo, A Iannuzzo, M Monaco, et al. Rocking of a rigid block freestanding on a flat pedestal. Journal of Zhejiang University. Science A, 2018, 19(5): 331–345 https://doi.org/10.1631/jzus.A1700061
24	M S Vassiliou, N Makris. Estimating time scales and length scales in pulselike earthquake acceleration records with wavelet analysis. Bulletin of the Seismological Society of America, 2011, 101(2): 596–618 https://doi.org/10.1785/0120090387
25	N Makris, M S Vassiliou. Planar rocking response and stability analysis of an array of free-standing columns capped with a freely supported rigid beam. Earthquake Engineering & Structural Dynamics, 2013, 42(3): 431–449 https://doi.org/10.1002/eqe.2222
26	S Li, C Zhai, L L Xie. Analysis on response of dynamic systems to pulse sequences excitation. International Journal of Advanced Structural Engineering, 2009, 1(1): 3–15
27	G Mylonakis, E Voyagaki. Yielding oscillator subjected to simple pulse waveforms: Numerical analysis and closed-form solutions. Earthquake Engineering & Structural Dynamics, 2006, 35(15): 1949–1974 https://doi.org/10.1002/eqe.615
28	A Gesualdo, A Iannuzzo, M Monaco, et al. Dynamic analysis offreestanding rigid blocks. In: Proceedings of the 12th International Conference on Computational Structures Technology. Kippen: Civil Comp Press, 2014, 106 https://doi.org/10.4203/ccp.106.144
29	A Gesualdo, A Iannuzzo, M Modano, et al. Dynamic behaviour of two stacked rigid blocks. In: Proceedings of the 23rd Conference of the Italian Association of Theoretical and Applied Mechanics. 2017, 4: 778–791
30	G P Mavroeidis, A S Papageorgiou. A mathematical representation of near-fault ground motions. Bulletin of the Seismological Society of America, 2003, 93(3): 1099–1131 https://doi.org/10.1785/0120020100
31	G Augusti. Rigid-plastic structures subject to dynamic loads. Meccanica, 1970, 5(2): 74–84 https://doi.org/10.1007/BF02134211
32	I Bergamasco, A Gesualdo, A Iannuzzo, et al. An integrated approach to the conservation of the roofing structures in the Pompeian Domus. Journal of Cultural Heritage, 2018, 31: 141–151 https://doi.org/10.1016/j.culher.2017.12.006
33	M Guadagnuolo, M Monaco. Out of plane behaviour of unreinforced masonry walls. In: Proceedings of International Conference on Protection of Historical Buildings. Rome: CRC Press, 2009, 2: 1177–1180
34	J B Martin. The determination of mode shapes for dynamically loaded rigid-plastic structures. Meccanica, 1981, 16(1): 42–45 https://doi.org/10.1007/BF02128308
35	J B Martin. A displacement bound principle for inelastic continua subjected to certain classes of dynamic loading. Journal of Applied Mechanics, 1965, 32(1): 1–6 https://doi.org/10.1115/1.3625722
36	M Veljkovic, C Heistermann, W Husson, et al. High-strength Tower in Steel for Wind Turbines (HISTWIN). Final Report—RFSR-CT-2006-00031. Brussels: European Commission (RFCS). 2012

[1]	M. H. KORAYEM, H. N. RAHIMI. Nonlinear dynamic analysis for elastic robotic arms[J]. Front Mech Eng, 2011, 6(2): 219-228.
[2]	LU Yanjun, HEI Di, WANG Yuan, DAI Rong, LU Yanjun, LIU Heng, YU Lie. Stability and coupling dynamic behavior of nonlinear journal active electromagnetic bearing rotor system[J]. Front. Mech. Eng., 2008, 3(2): 193-199.
[3]	LU Yanjun, LIU Heng, YU Lie, LI Qi, JIANG Ming, ZHANG Zhiyu. Analysis of stability and nonlinear response of rotor system with elliptical sliding bearing supports[J]. Front. Mech. Eng., 2007, 2(1): 37-45.

Viewed

Full text

Abstract

Cited

Shared

Discussed