Unpublished Paper
Discrete Breathers in a Mass-in-Mass Chain with Hertzian Local Resonators
(2016)
Abstract
We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with
linear intersite coupling and nonlinear Hertzian local resonators, which is motivated by recent studies
of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the
existence of the 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 nite chain, where the displacement pro les of the breathers are localized around
one or two lattice sites. 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 identi ed localized modes, including
within settings that may be relevant to future experimental studies.
Keywords
- Pattern Formation and Solitons,
- (nlin.PS)
Disciplines
Publication Date
2016
Citation Information
Panos Kevrekidis, S. P. Wallen, J. Lee, D. Mei, et al.. "Discrete Breathers in a Mass-in-Mass Chain with Hertzian Local Resonators" (2016) Available at: http://works.bepress.com/panos_kevrekidis/400/