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Published on: September 26, 2014
Breathers in periodic granular chains with multiple band gaps
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
This study explores localized nonlinear breathing modes in granular chains. These intrinsic localized modes, particularly those from upper band edges, show surprising robustness, even with dissipation.
Area of Science:
- Physics
- Materials Science
- Nonlinear Dynamics
Background:
- Granular chains with periodic heterogeneity exhibit unique wave propagation phenomena.
- Localized nonlinear modes are crucial for energy localization and dissipation in discrete systems.
Purpose of the Study:
- Investigate localized nonlinear breathing modes in heterogeneous granular chains with periodic arrangements.
- Analyze the formation and characteristics of intrinsic localized modes (ILMs) in specific steel-aluminum configurations.
- Explore the role of higher-order band gaps and dissipation in the emergence and robustness of these modes.
Main Methods:
- Theoretical analysis of heterogeneous granular chains with periodic structures (3- and 4-bead periodicity).
- Numerical simulations employing system driving via actuators or modulational instabilities.
- Investigation of systems with one steel and two aluminum beads, and one steel and three aluminum beads.
- Inclusion and analysis of dissipation effects in numerical experiments.
Main Results:
- Emergence of higher-order band gaps in heterogeneous granular configurations.
- Bifurcation of intrinsic localized modes from the edges of upper and lower band gaps.
- ILMs bifurcating from upper band edges demonstrate unexpected robustness compared to those from lower band edges.
- Spontaneous formation of localized modes within nearest gaps observed through direct numerical simulations.
- Dissipation was found to play a role in the behavior of these localized modes.
Conclusions:
- Heterogeneous granular chains support robust localized nonlinear breathing modes.
- The location of bifurcation (upper vs. lower band edge) significantly impacts mode robustness.
- Numerical simulations confirm the spontaneous generation of ILMs and highlight the influence of dissipation.
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