Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments

Stylianos Tsakirtzis, Panagiotis N. Panagopoulos, Gaetan Kerschen, Oleg Gendelman, Alexander F. Vakakis, Lawrence A. Bergman

Research output: Contribution to journalArticlepeer-review

Abstract

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency-energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers.

Original languageEnglish (US)
Pages (from-to)285-318
Number of pages34
JournalNonlinear Dynamics
Volume48
Issue number3
DOIs
StatePublished - May 1 2007

Keywords

  • Essentially nonlinear attachments
  • Passive targeted energy transfer
  • Regular backbone branches
  • Singular backbone branches
  • Transient resonance captures

ASJC Scopus subject areas

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

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