A Nonlinear and Non-Ideal Wind Generator Supporting Structure

Article Preview

Abstract:

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

433-442

Citation:

Online since:

October 2006

Export:

Price:

[1] J.M. Balthazar, R.M.L.R.F. Brasil and F.J. Garzeri: On non-ideal simple portal frame structural model: experimental results under non-ideal excitation. Applied Mechanics and Materials, Vols. 1-2 (2004), 51-58.

DOI: 10.4028/www.scientific.net/amm.1-2.51

Google Scholar

[2] S. Chaterjee, A.K. Mallik and A. Ghosh: On Impact dampers for non-linear vibration systems. Journal of Sound and Vibration, Vol. 187 (1995), 403-420.

DOI: 10.1006/jsvi.1995.0532

Google Scholar

[3] S. Chaterjee, A.K. Mallik and A. Ghosh: Impact dampers for controlling self-excited oscillations. Journal of Sound and Vibration, Vol. 193 (1995), 1003-1014.

DOI: 10.1006/jsvi.1996.0327

Google Scholar

[4] M.R. Duncan, C.R. Wassgren and C. M Krousgrill: The damping performance of a single particle impact damper. Journal of Sound and Vibration (article in press).

DOI: 10.1016/j.jsv.2004.09.028

Google Scholar

[5] V.O. Kononenko: Vibrating Systems with Limited Power Supply. London, 1969, Iliffe Books.

Google Scholar

[6] I. Lavassas, G. Nikolaidis, P. Zervas, E. Efthimiou, I.N. Doudoumis and C.C. Baniotopoulos: Analysis and design of the prototype of a steel 1-MW wind turbine tower. Engineering Structures, Vol. 25 (2003) 1097-1106.

DOI: 10.1016/s0141-0296(03)00059-2

Google Scholar

[7] Kun S. Marhadi and K. Vikram: Particle impact damping: effect of mass ratio, material, and shape. Journal of Sound and Vibration, Vol. 283 (2005)433 -448.

DOI: 10.1016/j.jsv.2004.04.013

Google Scholar

[8] A.B. Nordmark: Non-periodic motion caused by grazing in a impact oscillator. Journal of Sound and Vibration, Vol. 145 (1991), 279-297.

DOI: 10.1016/0022-460x(91)90592-8

Google Scholar

[9] M. Saeki: Impact damping with granular materials in a horizontally vibrating system. Journal of Sound and Vibration, Vol. 251 (2002), 153-161.

DOI: 10.1006/jsvi.2001.3985

Google Scholar

[10] S.L.T. Souza, I.L. Caldas, J.M. Balthazar and R.M.L.R.F. Brasil: Analysis of regular and irregular dynamics of a non-ideal gear-rattling problem. Journal of the Brazilian Society of Mechanical Sciences, Vol. 24 (2002), 111-114.

DOI: 10.1590/s0100-73862002000200005

Google Scholar

[11] S.L.T. Souza, I.L. Caldas, J.M. Balthazar and R.M.L.R.F. Brasil: 2005. Impact dampers for controlling chaos in systems with limited power supply. Journal of Sound and Vibration, Vol. 279 (2005) 955-967.

DOI: 10.1016/j.jsv.2003.11.068

Google Scholar

[12] J. Warminski, J.M. Balthazar and R.M.L.R.F. Brasil: Vibrations of a non-ideal parametrically and self-excited model. Journal of Sound and Vibration, Vol. 245 (2001) 363-374.

DOI: 10.1006/jsvi.2000.3515

Google Scholar