Impulsive steering between coexisting stable periodic solutions with an application to vibrating plates

Daniel W.M. Veldman*, Rob H.B. Fey, Hans Zwart

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)

Abstract

Single-degree-of-freedom (single-DOF) nonlinear mechanical systems under periodic excitation may possess multiple coexisting stable periodic solutions. Depending on the application, one of these stable periodic solutions is desired. In energy-harvesting applications, the large-amplitude periodic solutions are preferred, and in vibration reduction problems, the small-amplitude periodic solutions are desired. We propose a method to design an impulsive force that will bring the system from an undesired to a desired stable periodic solution, which requires only limited information about the applied force. We illustrate our method for a single-degree-of-freedom model of a rectangular plate with geometric nonlinearity, which takes the form of a monostable forced Duffing equation with hardening nonlinearity.

Original languageEnglish
Article number011013
JournalJournal of computational and nonlinear dynamics
Volume12
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • coexisting periodic solutions
  • control of mechanical systems
  • domains of attraction
  • Duffing equation
  • nonlinear systems
  • plates

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