Discrete breathers in a mass-in-mass chain with Hertzian local resonators

S. P. Wallen, J. Lee, D. Mei, C. Chong, P. G. Kevrekidis, and N. Boechler
Phys. Rev. E 95, 022904 – Published 22 February 2017

Abstract

We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear, precompressed Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes in a finite chain, where the displacement profiles of the breathers are localized around one lattice site. We then analyze the frequency-amplitude dependence of the breathers by performing numerical continuation on a linear eigenmode (vanishing amplitude) solution of the system near the upper band gap edge. Finally, we use direct numerical integration of the equations of motion to demonstrate the formation and evolution of the identified localized modes in energy-conserving and dissipative scenarios, including within settings that may be relevant to future experimental studies.

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  • Received 11 May 2016
  • Revised 3 December 2016

DOI:https://doi.org/10.1103/PhysRevE.95.022904

©2017 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsNonlinear DynamicsCondensed Matter, Materials & Applied PhysicsPolymers & Soft MatterGeneral Physics

Authors & Affiliations

S. P. Wallen1, J. Lee2, D. Mei2, C. Chong3, P. G. Kevrekidis2, and N. Boechler1

  • 1Department of Mechanical Engineering, University of Washington, Seattle, Washington 98195, USA
  • 2Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
  • 3Department of Mathematics, Bowdoin College, Brunswick, Maine 04011, USA

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Issue

Vol. 95, Iss. 2 — February 2017

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