Semi-analytical method to study piecewise linear oscillators
Agustín Hernández Rocha, Damián H. Zanette, Marian Wiercigroch
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 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.
Topics & Concepts
BifurcationPiecewise linear functionNonlinear systemMathematicsPiecewiseControl theory (sociology)Mathematical analysisMatrix (chemical analysis)Period-doubling bifurcationSet (abstract data type)Applied mathematicsComputer sciencePhysicsControl (management)Composite materialMaterials scienceArtificial intelligenceProgramming languageQuantum mechanicsVibration and Dynamic AnalysisDynamics and Control of Mechanical SystemsGear and Bearing Dynamics Analysis