Loading...
Thumbnail Image
Publication

Traveling Waves and their Tails in Locally Resonant Granular Systems

Abstract
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. The first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier transformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of antiresonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.
Type
article
article
Date
2015-01-01
Publisher
Degree
Advisors
Rights
License
Research Projects
Organizational Units
Journal Issue
Embargo
DOI
Publisher Version
Embedded videos