Limit cycle oscillations at resonances

K Hellevik,O T Gudmestad

doi:10.1088/1757-899x/276/1/012020

K Hellevik, O T Gudmestad

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https://doi.org/10.1088/1757-899x/276/1/012020

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Abstract

This paper deals with limit cycles in one degree of freedom systems. The van der Pol equation is an example of an equation describing systems with clear limit cycles in the phase space (displacement-velocity 2 dimensional plane). In this paper, it is shown that a system with nonlinear loading, representing the drag load acting on structures in an oscillatory flow (the drag term of the Morison equation), will in fact exhibit limit cycles at resonance and at higher order resonances. These limit cycles are stable, and model self-excited oscillations. As the damping in the systems is linear and constant, the drag loading will to some degree work as negative damping. The consequences of the existence of these limit cycles are that systems starting at lesser amplitudes in the phase plane will exhibit increased amplitudes until the limit cycle is obtained.

Highlights

The phase plane is a plane where the system’s position and velocity are plotted for an increasing time, t
It is shown that a system with nonlinear loading, representing the drag load acting on structures in an oscillatory flow, will exhibit limit cycles at resonance and at higher order resonances
The phase plane method, which evolves around finding limit cycles, is adapted from Struble and Martin [1]

Summary

Limit cycle oscillations at resonances

To cite this article: K Hellevik and O T Gudmestad 2017 IOP Conf. View the article online for updates and enhancements. - Rydberg electrons in crossed fields: a paradigm for nonlinear dynamics beyond two degrees of freedom T Uzer. - The assessment of vibration absorption capacity of elevator's passengers I Herrera and S Kaczmarczyk. This content was downloaded from IP address 152.94.247.251 on 16/05/2018 at 12:09

Introduction

Published under licence by IOP Publishing Ltd

Conclusions