Computation of Periodic Orbits for Piecewise Linear Oscillator by Harmonic Balance Methods Communications in Nonlinear Science and Numerical Simulation

Lijun Pei, Antonio Simon Chong Escobar, Ekaterina Pavlovskaia, Marian Wiercigroch* (Corresponding Author)

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, Harmonic Balance based methods, namely Incremental Harmonic Balance Method and the method of Harmonic Balance with Alternating Frequency and Time traditionally used to compute periodic orbits of smooth nonlinear dynamical systems are employed to investigate dynamics of a non-smooth system, a piecewise linear oscillator with a play. The Incremental Harmonic Balance Method was used to compute the period one orbits including those exhibiting grazing and large impacts. The method of Harmonic Balance with Alternating Frequency and Time was implemented to calculate more complex orbits and multi stability. A good agreement between obtained approximate solutions and numerically calculated responses indicates robustness of the implemented HBMs, which should allow to effectively study the global dynamics of non-smooth systems.
Original languageEnglish
JournalCommunications in Nonlinear Science & Numerical Simulation
Publication statusAccepted/In press - 24 Dec 2021

Keywords

  • Piecewise linear oscillator with play
  • Incremental Harmonic Balance Method
  • IHBM
  • Harmonic Balance with Alternative Frequency and Time
  • HB-AFT
  • Computation of periodic orbits

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