Floquet-type analysis of transient vibrations of a horizontal axis wind turbine

Gizem D. Acar, Brian F. Feeny

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

General responses of coupled blade-hub equations of a horizontal axis wind turbine (HAWT) are studied. HAWT blades have parametric stiffness terms due to gravity. The blade equations are coupled through the rotor equation, and blade stiffness varies cyclically with the hub angle. In this study, the equations of motion are transformed from the time domain to the hub angle domain, and a scaling scheme is used which results in interdependent blade equations and eliminates the rotor equation. With hub angle as the independent coordinate, the blade equations have parametric stiffness. Then, assuming a Floquet-type solution, unforced dynamics of a turbine is investigated. The assumed solution is a product between an exponential and a periodic part. Plugging into the equations of motion, and applying harmonic balance method, an eigenvalue problem is obtained in terms of system parameters, where the eigenvalues are the characteristic exponents in the exponential part of the assumed solution. The solution to the eigenvalue problem provides parametric modal solutions. The response to an arbitrary initial condition is approximated by combining the modal solutions. Additionally, stability of the solutions is investigated by examining the characteristic exponents. The results are then compared to numerical solutions for verification.

Original languageEnglish
Title of host publicationTopics in Modal Analysis and Testing, Volume 9 - Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018
EditorsMichael Mains, Brandon J. Dilworth
Pages329-333
Number of pages5
DOIs
StatePublished - 2019
Event36th IMAC, A Conference and Exposition on Structural Dynamics, 2018 - FL, United States
Duration: 12 Feb 201815 Feb 2018

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
Volume9
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Conference

Conference36th IMAC, A Conference and Exposition on Structural Dynamics, 2018
Country/TerritoryUnited States
CityFL
Period12/02/1815/02/18

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