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

Brian Feeny

Professor, Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824

1Corresponding author.

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


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.

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