Semi-analytical method to study piecewise linear oscillators

Agustín  Hernández Rocha; Damián H.  Zanette; Marian Wiercigroch

doi:10.1016/j.cnsns.2023.107193

Semi-analytical method to study piecewise linear oscillators

Agustín Hernández Rocha, Damián H. Zanette, Marian Wiercigroch

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Abstract

This article proposes a semi-analytical method to investigate the dynamics and
bifurcation scenarios of piecewise linear oscillators. The method is based on a mapping technique with a matrix structure that allows easy and rapid construction of any periodic orbit. When validated against direct numerical integration simulations, a good correlation and an accurate prediction of bifurcation phenomena were shown. The method is applied to analyze the nonlinear dynamic responses and bifurcations scenarios causes by changes of stiffness and viscous damping. A set of minimum conditions that the system must meet to present period doubling bifurcations and sub-harmonic orbits was given.

Original language	English
Article number	107193
Number of pages	20
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	121
Early online date	13 Mar 2023
DOIs	https://doi.org/10.1016/j.cnsns.2023.107193
Publication status	Published - 15 Jun 2023

Bibliographical note

Acknowledgements
The authors would like to thank the Balseiro Institute and the National Commission
of Atomic Energy for the support. In particular, financial support for the Invited Professor Programme of the Balseiro Institute, which made international collaboration possible.

Data Availability Statement

No data was used for the research described in the article.

Keywords

Piecewise linear oscillator
Semi-analytical solution
numerical simulation
non-linear dynamics analysis

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Cite this

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AU - Zanette, Damián H.

AU - Wiercigroch, Marian

N1 - Acknowledgements The authors would like to thank the Balseiro Institute and the National Commission of Atomic Energy for the support. In particular, financial support for the Invited Professor Programme of the Balseiro Institute, which made international collaboration possible.

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N2 - This article proposes a semi-analytical method to investigate the dynamics andbifurcation scenarios of piecewise linear oscillators. The method is based on a mapping technique with a matrix structure that allows easy and rapid construction of any periodic orbit. When validated against direct numerical integration simulations, a good correlation and an accurate prediction of bifurcation phenomena were shown. The method is applied to analyze the nonlinear dynamic responses and bifurcations scenarios causes by changes of stiffness and viscous damping. A set of minimum conditions that the system must meet to present period doubling bifurcations and sub-harmonic orbits was given.

AB - This article proposes a semi-analytical method to investigate the dynamics andbifurcation scenarios of piecewise linear oscillators. The method is based on a mapping technique with a matrix structure that allows easy and rapid construction of any periodic orbit. When validated against direct numerical integration simulations, a good correlation and an accurate prediction of bifurcation phenomena were shown. The method is applied to analyze the nonlinear dynamic responses and bifurcations scenarios causes by changes of stiffness and viscous damping. A set of minimum conditions that the system must meet to present period doubling bifurcations and sub-harmonic orbits was given.

KW - Piecewise linear oscillator

KW - Semi-analytical solution

KW - numerical simulation

KW - non-linear dynamics analysis

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DO - 10.1016/j.cnsns.2023.107193

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JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 107193

ER -

Semi-analytical method to study piecewise linear oscillators

Abstract

Bibliographical note

Data Availability Statement

Keywords

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