Discrete Breathers in One-Dimensional Diatomic Granular Crystals

Abstract

We report the experimental observation of discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families of solutions we compute throughout the linear spectral gap. Finally, we observe experimentally such localized breathing modes with quantitative characteristics that agree with our numerical results.

Dark breathers in granular crystals

“…For that reason the latter have only been identified in heterogeneous configurations with different periodicities [19][20][21], or in monomer settings bearing defects [18]. In the latter case, localization is not intrinsic to the chain but rather is supported as an impurity mode by the defect.…”

“…1 for an example. Although bright discrete breathers are known to exist in granular crystals (in dimer or higher periodic configurations, and in monomer chains with defects, for example [18][19][20][21]), the * chong@math.umass.edu; http://www.math.umass.edu/∼chong properties of dark discrete breathers in granular crystals remain an open question and are the subject of this work.…”

“…These topics form the focus of the present work. Although the homogeneous chain is the sole configuration considered here, it is important to note that dark breathers may exist in other configurations, such as the defect [18] and periodic chains [19][20][21] mentioned above.…”

Mechanical wave propagation within nanogold granular crystals

“…Another fascination of granular crystals is the construction of diatomic lattices composed of alternating granules of two different properties such as shape, stiffness and mass etc, adding to the tunability of mechanical waves to a great extent. For example, in compressed diatomic chains of alternating steel and aluminum spherical granules, the existence of discrete breathers was theoretically and experimentally proved, where sustained, exponentially localized oscillations emerge at a frequency inside the forbidden band of the linear Fourier spectrum 31 . For uncompressed diatomic lattices assembled by two different masses, strongly nonlinear resonances and anti-resonances are described by theory and experiments, resulting in 4 an optimal wave attenuation and a new type of solitary wave respectively [32][33][34] .…”

Wave propagation in one-dimensional microscopic granular chains

“…Macroscopic granular crystals, composed of particles in the centimeter scale, have been subject of active research [1][2][3][4][5][6]. Granular crystals have been shown to mediate nonlinear wave phenomena such as solitary waves [1] and intrinsic localized modes [7], which are of fundamental scientific interest.…”