Abstract
General responses of multi-degrees-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 is found. Solving the eigenvalue problem, frequency content of the solution and response to arbitrary initial conditions are determined. Using the eigenvalues and the eigenvectors, the system response is written in terms of “Floquet modes,” which are nonsynchronous, 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.