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

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

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

Fingerprint

Periodic Solution
Energy harvesting
Hardening
Degree of freedom
Geometric Nonlinearity
Duffing Equation
Energy Harvesting
Rectangular Plate
Mechanical Systems
Nonlinear Systems
Vibration
Excitation
Nonlinearity
Model

Keywords

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

Cite this

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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.",
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Impulsive steering between coexisting stable periodic solutions with an application to vibrating plates. / Veldman, Daniel W.M.; Fey, Rob H.B.; Zwart, Hans.

In: Journal of computational and nonlinear dynamics, Vol. 12, No. 1, 011013, 01.01.2017.

Research output: Contribution to journalArticleAcademicpeer-review

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