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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Limit Cycle Prediction for a Multi-Degree-of-Freedom System with a Freeplay Non-Linearity

Journal of Applied Nonlinear Dynamics 12(2) (2023) 379--403 | DOI:10.5890/JAND.2023.06.014

A. P. Lewis

School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield, Hertfordshire AL10 9AB, United Kingdom

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Abstract

This paper presents a method for predicting limit cycles of a multi-degree-of-freedom system possessing a freeplay non-linearity. The approach taken is through casting the problem as an integro-differential equation. The method is a development of that previously reported in the literature for the simpler case of such a system with a cubic hardening non-linearity. The system considered is based on aeroelastic applications where structural non-linearities of this kind are encountered. Limit cycles stability is determined using an implementation of Floquet analysis based on extending the Hill's Determinant approach that may be used in analysing the Mathieu equation. The limit cycle predictions and Floquet multipliers are compared against predictions from numerical integration to show the validity of the method. Fast Fourier transform analysis is used to provide comparisons with the predictions of harmonic components from the analytical results. As the Floquet analysis also produces an approximation to the motion of the system in the neighbourhood of a limit cycle, in the case of an unstable limit cycle, it was possible to approximate the limit cycle stable manifold in situations where the limit cycle amplitude is much greater than the amount of freeplay.

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