Semi-analytical method to study piecewise linear oscillators

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 numeri...

Full description

Saved in:

Bibliographic Details
Published in:	Communications in nonlinear science & numerical simulation Vol. 121; p. 107193
Main Authors:	Hernández Rocha, Agustín, Zanette, Damián H., Wiercigroch, Marian
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 15-06-2023
Subjects:	Nonlinear dynamics analysis Numerical simulation Piecewise linear oscillator Semi-analytical solution Semi-analytical solution Numerical simulation Nonlinear dynamics analysis Piecewise linear oscillator
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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 analyse 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. •A semi-analytical method to compute any periodic orbit of a piecewise linear oscillator was developed.•Non-physical solutions generated by the method were identified and described.•A set of minimum conditions the system to exhibit period doubling bifurcations and sub-harmonic orbits was given.
ISSN:	1007-5704 1878-7274
DOI:	10.1016/j.cnsns.2023.107193