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.

We present a model for wave propagation in a monolayer of spheres on an elastic substrate. The model, which considers sagittally polarized waves, includes: horizontal, vertical, and rotational degrees of freedom; normal and shear coupling between the spheres and substrate, as well as between adjacent spheres; and the effects of wave propagation in the elastic substrate. For a monolayer of interacting spheres, we find three contact resonances, whose frequencies are given by simple closedform expressions. For a monolayer of isolated spheres, only two resonances are present. The contact resonances couple to surface acoustic waves in the substrate, leading to mode hybridization and "avoided crossing" phenomena. We present dispersion curves for a monolayer of silica microspheres on a silica substrate, assuming adhesive Hertzian interactions, and compare calculations using an effective medium approximation (including elasticity of the substrate) to a discrete model of a monolayer on a rigid substrate. While the effective medium model does not describe discrete lattice effects occurring at short wavelengths, we find that it is well suited for describing the interaction between the monolayer and substrate in the long wavelength limit. We suggest that a complete picture of the dynamics of a monolayer adhered to an elastic substrate can be found by combining the dispersion curves generated with the effective medium model for the elastic substrate and with the discrete model for the rigid substrate. This model is potentially scalable for use with nano-to macroscale systems, and offers the prospect of experimentally extracting contact stiffnesses from measurements of acoustic dispersion.

We report the design and characterization of a self-assembled, locally resonant acoustic metamaterial for Lamb waves, composed of a monolayer of 1.02 µm polystyrene microspheres adhered to a 1.3 µm thick free-standing silicon membrane. A laser-induced transient grating technique is used to generate Lamb waves in the metamaterial and measure its acoustic response. The measurements reveal a microsphere contact resonance and the lowest frequency spheroidal microsphere resonance. The measured dispersion curves show hybridization of flexural Lamb waves with the microsphere contact resonance. We compare the measured dispersion with an analytical model using the contact resonance frequency as a single fitting parameter, and find that it well describes the observed hybridization. Results from this study can lead to an improved understanding of microscale contact mechanics and to the design of new types of acoustic metamaterials.

International audienceWe present a method for the recovery of complex wavenumber information via spatial Laplace transforms of spatiotemporal wave propagation measurements. The method aids in the analysis of acoustic attenuation phenomena and is applied in three different scenarios: (i) Lamb-like modes in air-saturated porous materials in the low kHz regime, where the method enables the recovery of viscoelastic parameters; (ii) Lamb modes in a Duralumin plate in the MHz regime, where the method demonstrates the effect of leakage on the splitting of the forward S-1 and backward S-2 modes around the Zero-Group Velocity point; and (iii) surface acoustic waves in a two-dimensional microscale granular crystal adhered to a substrate near 100 MHz, where the method reveals the complex wave-numbers for an out-of-plane translational and two in-plane translational-rotational resonances. This method provides physical insight into each system and serves as a unique tool for analyzing spatiotemporal measurements of propagating waves. Published by AIP Publishing

Acoustic non-reciprocity has been shown to enable a plethora of effects analogous to phenomena seen in quantum physics and electromagnetics, such as immunity from back-scattering and unidirectional band gaps, which could lead to the design of direction-dependent acoustic devices. One way to break reciprocity is by spatiotemporally modulating material properties, which breaks parity and time-reversal symmetries. In this work, we present a model for a medium in which a slow, nonlinear deformation modulates the effective material properties for small, overlaid disturbances (often referred to as 'small-on-large' propagation). The medium is modeled as a discrete spring-mass chain that undergoes large deformation via prescribed displacements of certain points in the unit cell. A multiple-scale perturbation analysis shows that, for sufficiently slow modulations, the small-scale waves can be described by a linear, monatomic chain with time-and space-dependent on-site stiffness. The modulation depth can be tuned by changing the geometric and stiffness parameters of the unit cell. The accuracy of the small-on-large approximation is demonstrated using direct numerical simulations.