Interactions of propagating waves in a one-dimensional chain of linear oscillators with a strongly nonlinear local attachment

Alexander F. Vakakis, Mohammad A. Al-Shudeifat, M. Arif Hasan

Research output: Contribution to journalArticle

Abstract

We study the interaction of propagating wavetrains in a one-dimensional chain of coupled linear damped oscillators with a strongly nonlinear, lightweight, dissipative local attachment which acts, in essence, as nonlinear energy sink - NES. Both symmetric and highly un-symmetric NES configurations are considered, labelled S-NES and U-NES, respectively, with strong (in fact, non-linearizable or nearly non-linearizable) stiffness nonlinearity. Especially for the case of U-NES we show that it is capable of effectively arresting incoming slowly modulated pulses with a single fast frequency by scattering the energy of the pulse to a range of frequencies, by locally dissipating a major portion of the incoming energy, and then by backscattering residual waves upstream. As a result, the wave transmission past the location of the NES is minimized, and the NES acts, in effect, as passive wave arrestor and reflector. Analytical reduced-order modeling of the dynamics is performed through complexification/averaging. In addition, governing nonlinear dynamics is studied computationally and compared to the analytical predictions. Results from the reduced order model recover the exact computational simulations.

Original languageEnglish (US)
Pages (from-to)2375-2397
Number of pages23
JournalMeccanica
Volume49
Issue number10
DOIs
StatePublished - Oct 2014

Keywords

  • Nonlinear energy sink
  • Passive wave arrest
  • Strong nonlinearity
  • Targeted energy transfer

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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