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.

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstrain. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.

The features of solitary waves observed in horizontal monodisperse chain of barely touching beads not only depend on geometrical and material properties of the beads but also on the initial perturbation provided at the edge of the chain. An impact of a large striker on a monodisperse chain, and similarly a sharp decrease of bead radius in a stepped chain, generates a solitary wave train containing many single solitary waves ordered by decreasing amplitudes. We find, by simple analytical arguments, that the unloading of compression force at the chain edge has a nearly exponential decrease. The characteristic time is mainly a function involving the grains' masses and the striker mass. Numerical calculations and experiments corroborate these findings.

We present an experimental study of the mechanical impulse propagation through a horizontal alignment of elastic spheres of progressively decreasing diameter phi(n): namely, a tapered chain. Experimentally, the diameters of spheres which interact via the Hertz potential are selected to keep as close as possible to an exponential decrease, phi(n+1) = (1-q)phi(n), where the experimental tapering factor is either q(1) approximately equal to 5.60% or q(2) approximately equal to 8.27%. In agreement with recent numerical results, an impulse initiated in a monodisperse chain (a chain of identical beads) propagates without shape changes and progressively transfers its energy and momentum to a propagating tail when it further travels in a tapered chain. As a result, the front pulse of this wave decreases in amplitude and accelerates. Both effects are satisfactorily described by the hard-sphere approximation, and basically, the shock mitigation is due to partial transmissions, from one bead to the next, of momentum and energy of the front pulse. In addition when small dissipation is included, better agreement with experiments is found. A close analysis of the loading part of the experimental pulses demonstrates that the front wave adopts a self-similar solution as it propagates in the tapered chain. Finally, our results corroborate the capability of these chains to thermalize propagating impulses and thereby act as shock absorbing devices.

We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: ͑1͒ an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and ͑2͒ a potentially stable discrete gap breather that is centered on a light particle and is characterized by an asymmetric spatial energy profile. We investigate their existence, structure, and stability throughout the band gap of the linear spectrum and classify them into four regimes: a regime near the lower optical band edge of the linear spectrum, a moderately discrete regime, a strongly discrete regime that lies deep within the band gap of the linearized version of the system, and a regime near the upper acoustic band edge. We contrast discrete breathers in anharmonic Fermi-Pasta-Ulam ͑FPU͒-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and note that the asymmetric nature of the tensionless interaction potential can lead to hybrid bulk-surface localized solutions.

We investigate the dynamical response of a mass defect in a one-dimensional non-loaded horizontal chain of identical spheres which interact via the nonlinear Hertz potential. Our experiments show that the interaction of a solitary wave with a light intruder excites localized mode. In agreement with dimensional analysis, we find that the frequency of localized oscillations exceeds the incident wave frequency spectrum and nonlinearly depends on the size of the intruder and on the incident wave strength. The absence of tensile stress between grains allows some gaps to open, which in turn induce a significant enhancement of the oscillations amplitude. We performed numerical simulations that precisely describe our observations without any adjusting parameters. [3]. For example, the presence of an isotope in a perfect linear crystal is known to enhance optical waves absorption at given frequencies [4]. One-dimensional chains of beads interacting via the Hertz potential are systems suitable to observe nonlinear localization effects. A loaded chain of identical beads is dispersive, allowing small perturbations to propagate as linear or weakly nonlinear acoustic waves [5]. In contrast, when grains in a chain barely touch one another, the energy of an impulse only propagates as fully nonlinear solitary waves [5,6,7] resulting from the balance between dispersion and nonlinearity of the medium. Nesterenko early described this regime as a sonic vacuum limit [8]. Dissipative effects such as viscoelasticity or friction only attenuate and spread these solitary waves [7,9]. In contrast, any heterogeneity of the medium capable of unbalancing dispersion and nonlinearity results in breaking the solitary wave symmetry. For example, a narrow pulse propagating in a chain of beads with decreasing sizes develops a long tail which spreads in time the momentum transfer [10,11,12]. Designing powerfull impact protection systems takes advantage of these features [10,11,13]. Granular chains made of successions of heavy and light beads also proved valuable efficiency in energy absorption [14]. More recently, fully nonlinear waves with finite-width were observed in chains containing periodic mass defects or soft inclusions [15]. Such nonlinear dimer chains are expected to support additionnal optical modes and forbidden band gap when subjected to a static load [15].The elementary interaction of either lighter or heavier intruders with solitary waves in non-loaded monodisperse chains of beads has been investigated numerically [16]. When a solitary wave reaches a mass defect, energy is partially reflected into a backward traveling solitary wave and is partially transmitted to the intruder. A heavy impurity slowly translates, leading to a large transmitted solitary waves train in the forward direction [16], similarly to what was observed in stepped chains [5,8,12]. A light intruder oscillates and scatters forward and backward weak delayed solitary waves trains [16].In this letter, we investigate experimentally the interaction of a solitary wave wi...

We study experimentally the interaction between two solitary waves that approach one another in a linear chain of spheres interacting via the Hertz potential. When these counterpropagating waves collide, they cross each other and a phase shift in respect to the noninteracting waves is introduced as a result of the nonlinear interaction potential. This observation is well reproduced by our numerical simulations and is shown to be independent of viscoelastic dissipation at the bead contact. In addition, when the collision of equal amplitude and synchronized counterpropagating waves takes place, we observe that two secondary solitary waves emerge from the interacting region. The amplitude of the secondary solitary waves is proportional to the amplitude of incident waves. However, secondary solitary waves are stronger when the collision occurs at the middle contact in chains with an even number of beads. Although numerical simulations correctly predict the existence of these waves, experiments show that their respective amplitudes are significantly larger than predicted. We attribute this discrepancy to the rolling friction at the bead contact during solitary wave propagation.

It is demonstrated that the temperature oscillations near the edge of the thermoacoustic stack are highly anharmonic even in the case of harmonic acoustic oscillations in the thermoacoustic engines. In the optimum regime for the acoustically induced heat transfer, the amplitude of the second harmonic of the temperature oscillations is comparable to that of the fundamental frequency.