0
research-article

Approximate Floquet Analysis of Parametrically Excited Multi-Degree-of-Freedom Systems with Application to Wind Turbines

[+] Author and Article Information
Gizem Acar

Postdoctoral Research Associate, Dynamics and Control Laboratory, Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742
gizem@umd.edu

Brian Feeny

Professor, Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824
feeny@egr.msu.edu

1Corresponding author.

ASME doi:10.1115/1.4040522 History: Received March 14, 2018; Revised June 04, 2018

Abstract

General responses of multi-degree-of-freedom (MDOF) systems with parametric stiffness are studied. A Floquet-type solution, which is a product between an exponential part and a periodic part, is assumed, and applying harmonic balance, an eigenvalue problem (EVP) is found. Solving the EVP, frequency content of the solution, and response to random initial conditions are determined. Using the eigenvalues and the eigenvectors, the system response is written in terms of "Floquet modes", which are non-synchronous, contrary to linear modes. Studying the eigenvalues (i.e. characteristic exponents), stability of the solution is investigated. The approach is applied to MDOF systems, including an example of a three-blade wind turbine, where the equations of motion have parametric stiffness terms due to gravity. The analytical solutions are also compared to numerical simulations for verification.

Copyright (c) 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In