Suppressing homoclinic chaos for a weak periodically excited non-smooth oscillator

Shuangbao Li, Xixi Ma, Xiaoli Bian, Siu Kai Lai, Wei Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

In this work, some new effective methods for suppressing homoclinic chaos in a weak periodically excited non-smooth oscillator are studied, and the main idea is to modify slightly the Melnikov function such that the zeros are eliminated. Firstly, a general form of planar piecewise-smooth oscillators is given to approximatively model many nonlinear restoring force of smooth oscillators subjected to all kinds of damping and periodic excitations. In the absence of controls, the Melnikov method for non-smooth homoclinic trajectories within the framework of a piecewise-smooth oscillator is briefly introduced without detailed derivation. This analytical tool is useful to detect the threshold of parameters for the existence of homoclinic chaos in the non-smooth oscillator. After some methods of state feedback control, self-adaptive control and parametric excitations control are, respectively, considered, sufficient criteria for suppressing homoclinic chaos are derived by employing the Melnikov function of non-smooth systems. Finally, the effectiveness of strategies for suppressing homoclinic chaos is analytically and numerically demonstrated through a specific example.

Original languageEnglish
Pages (from-to)1621-1642
Number of pages22
JournalNonlinear Dynamics
Volume99
Issue number2
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Homoclinic chaos
  • Melnikov method
  • Non-smooth oscillators
  • Suppressing chaos

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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