Observation of the Sommerfeld Effect in Wind Turbine Towers
Bruno Roberto Ferreira1; Reyolando M. L. R. F. Brasil1
1 Federal University of ABC
doi:10.20906/CPS/CILAMCE2017-0072
Resumo
Discontinuities and "jumps" have been observed in nonlinear oscillations theory studies. These phenomena in the nonlinear dynamics of structures are especially seen when the structure interacts with an oscillating energy source. One case of this kind of behavior, that has been discussed by Kononenko (1969), is a structural system excited by a non-ideal limited power supply, in which it is possible to observe these "jumps" in the resonance curve of the system, called the Sommerfeld effect. Our model is a wind turbine tower and rotor whose dynamic behaviour is very likely to present these phenomena, due to the considerable height of the tower, which reflects on its mechanical proprieties. This research intends to show possible interaction between the power supply and the structure and point out and analyse the discontinuities. We also evaluate if there are any possible structural risk outcoming from these oscillations. A one degree of freedom model was utilized to represent the system, and the equations of motion were obtained by the formulation of Lagrange. Afterwards, its numerical solutions were obtained. Some key parameters of the oscillation study, as the natural frequency of the system, were obtained using the Rayleigh method. From the observation of the resonance curves obtained it is expected to be observed the Sommerfeld effect and how it impacts the system in such cases, as well as if the results resemble the ones obtained in the literature of similar cases.
Palavras-chave: nonlinear dynamics; Non-ideal power supply; Sommerfeld effect; wind turbines; Rayleigh's method