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research-article

Parametric Instability and Localization of Vibrations in Three-Blade Wind Turbines

[+] Author and Article Information
Takashi Ikeda

Department of Mechanical Systems Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527 Japan
tikeda@hiroshima-u.ac.jp

Yuji Harata

Department of Mechanical Systems Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527 Japan
harata@hiroshima-u.ac.jp

Yukio Ishida

Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601 Japan
ishida@nuem.nagoya-u.ac.jp

1Corresponding author.

ASME doi:10.1115/1.4039899 History: Received July 06, 2017; Revised March 22, 2018

Abstract

Nonlinear vibration characteristics of three-blade wind turbines are theoretically investigated. The wind turbine is modeled as a coupled system, consisting of a flexible tower with two degrees of freedom (2DOF), and three blades, each with a single degree of freedom (SDOF). The blades are subjected to steady winds. The wind velocity increases proportionally with height due to vertical wind shear. The natural frequency diagram is calculated with respect to the rotational speed of the wind turbine. The corresponding linear system with parametric excitation terms is analyzed to determine the rotational speeds where unstable vibrations appear and to predict at what rotational speeds the blades may vibrate at high amplitudes in a real wind turbine. The frequency response curves are then obtained by applying the swept-sine test to the equations of motion for the nonlinear system. They exhibit softening behavior due to the nonlinear restoring moments acting on the blades. Stationary time histories and their fast Fourier transform (FFT) results are also calculated. In the numerical simulations, localization phenomena are observed, where the three blades vibrate at different amplitudes. Basins of attraction (BOAs) are also calculated to examine the influence of a disturbance on the appearance of localization phenomena.

Copyright (c) 2018 by ASME
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