Bend-bend-twist vibrations of a wind turbine blade

Gizem D. Acar, Brian F. Feeny

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Dynamics of a wind turbine blade under bend-bend-twist coupled vibrations is investigated. The potential and kinetic energy expressions for a straight nonuniform blade are written in terms of beam parameters. Then, the energies are expressed in terms of modal coordinates by using the assumed mode method, and the equations of motion are found by applying Lagrange's formula. The bend-bend-twist equations are coupled with each other and have stiffness variations due to centrifugal effects and gravitational parametric terms, which vary cyclicly with the hub angle. To determine the natural frequencies and mode shapes of the system, a modal analysis is applied on the linearized coupled equations of constant angle snapshots of a blade with effects of constant speed rotation. Lower modes of the coupled bend-bend-twist model are dominantly in-plane or out-of-plane modes. To investigate the parametric effects, several blade models are analyzed at different angular positions. The stiffness terms involving centrifugal and gravitational effects can be significant for long blades. To further see the effect of blade length on relative parametric stiffness change, the blade models are scaled in size and analyzed at constant rotational speeds, at horizontal and vertical orientations. These studies show that the parametric stiffness effects should be taken into account when designing long blades.

Original languageEnglish
Pages (from-to)15-28
Number of pages14
JournalWind Energy
Volume21
Issue number1
DOIs
StatePublished - Jan 2018

Keywords

  • blade vibrations
  • modal analysis
  • parametric excitation

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