Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals with Three-Particle Unit Cells

We investigate the tunable vibration filtering properties of one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (steel-cylinder-sphere) in which the length of the cylinder is varied systematically. We apply static compression to linearize the dynamic response of the crystals and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of up to three distinct pass bands and two finite band gaps and show their tunability for variations in cylinder length and static compression

Defect Modes in One-Dimensional Granular Crystals

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We measure the near-linear frequency spectrum within the spatial vicinity of the defects, and identify the frequencies of the localized defect modes. We compare the experimentally determined frequencies with those obtained by numerical eigen-analysis and by analytical expressions based on few-site considerations. We also present a brief numerical and experimental example of the nonlinear generalization of a single-defect localized mode

Discrete Breathers in One-Dimensional Diatomic Granular Crystals

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.Comment: 5 pages, 4 figure

Engineering task plan for AX-104 residual waste volume and inventory data collection

The purpose of this Engineering Task Plan is to document the strategy, equipment and responsibilities of the tasks required to preform the volume and inventory data collection of tank AX-104. The project is a part of the Hanford Tanks Initiative Plan document number WHC-SD-WM-PMP-022 Revision D

Hydrogen Interaction with Platinum and Palladium Surfaces

Platinum and palladium surfaces are utilized as catalytic surfaces in the chemical industry. Understanding how hydrogen atoms interact with the metal surfaces will allow for further advancement in this area. Specifically, the interaction of hydrogen on the surface and subsurface of these metals was investigated using density functional theory calculations through Python scripts and the VASP software. The tests concluded that the hydrogen adsorption is favorable on the surface of both metals, but only on the subsurface of palladium. In addition, when more than one atom of hydrogen was introduced to the metal, the two hydrogen atoms demonstrated repulsive effects on one another.Key Words: Platinum, Palladium, catalytic surfaces, hydrogen ato

Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves

Contact-based vibrations play an essential role in the dynamics of granular materials. Significant insights into vibrational granular dynamics have previously been obtained with reduced-dimensional systems containing macroscale particles. We study contact-based vibrations of a two-dimensional monolayer of micron-sized spheres on a solid substrate that forms a microscale granular crystal. Measurements of the resonant attenuation of laser-generated surface acoustic waves reveal three collective vibrational modes that involve displacements and rotations of the microspheres, as well as interparticle and particle-substrate interactions. To identify the modes, we tune the interparticle stiffness, which shifts the frequency of the horizontal-rotational resonances while leaving the vertical resonance unaffected. From the measured contact resonance frequencies we determine both particle-substrate and interparticle contact stiffnesses and find that the former is an order of magnitude larger than the latter. This study paves the way for investigating complex contact-based dynamics of microscale granular crystals and yields a new approach to studying micro- to nanoscale contact mechanics in multiparticle networks.National Science Foundation (U.S.) (Grant CMMI-1333858)United States. Army Research Office (Grant W911NF-15-1-0030)University of Washington. Royalty Research FoundationNational Science Foundation (U.S.) (Grant CHE-1111557

Breathers In Periodic Granular Chains With Multiple Band Gaps

We consider the localized nonlinear breathing modes that emerge in heterogeneous granular configurations of two materials with a periodicity of three and four beads. We examine as characteristic examples chains with 1 steel and 2 alumnium beads, as well as ones with 1 steel and three aluminum beads. We analyze the higher order gaps that emerge in such settings and explore the intrinsic localized modes that bifurcate from the edge of the upper bands. A generic surprising feature of such states is that they appear to be more robust than their counterparts bifurcating from the edges of the lower bands. Direct numerical simulations, using driving of the system at suitable frequencies through an actuator or taking advantage of the modulational instabilities of extended band edge states in the system illustrate the spontaneous formation of localized modes within the corresponding nearest gaps

Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals

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: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) 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 FPU-type diatomic chains with those in diatomic granular crystals, which have a tensionless interaction potential between adjacent particles, and highlight in that the asymmetric nature of the latter interaction potential may lead to a form of hybrid bulk-surface localized solutions

Vibrational dynamics of a two-dimensional microgranular crystal

We study the dynamics of an ordered hexagonal monolayer of polystyrene microspheres adhered to a glass substrate coated with a thin aluminum layer. A laser-induced transient grating technique is employed to generate and detect three types of acoustic modes across the entire Brillouin zone in the Γ−K direction: low-frequency contact-based modes of the granular monolayer, high-frequency modes originating from spheroidal vibrations of the microspheres, and surface Rayleigh waves. The dispersion relation of contact-based and spheroidal modes indicates that they are collective modes of the microgranular crystal controlled by particle-particle contacts. We observe a spheroidal resonance splitting caused by the symmetry breaking due to the substrate, as well as an avoided crossing between the Rayleigh and spheroidal modes. The measurements are found to be in agreement with our analytical model.United States. Department of Energy (Grant DE-FG02-00ER15087)National Science Foundation (U.S.) (Grant CHE-1111557