Energy spreading, equipartition and chaos in lattices with non-central forces

We numerically study a one dimensional, nonlinear lattice model which in the linear limit is relevant to the study of bending (flexural) waves. In contrast with the classic one dimensional mass-spring system, the linear dispersion relation of the considered model has different characteristics in the low frequency limit. By introducing disorder in the masses of the lattice particles, we investigate how different nonlinearities (cubic, quadratic and their combination) lead to energy delocalization, equipartition and chaotic dynamics. We excite the lattice using single site initial momentum excitations corresponding to a strongly localized linear mode and increase the initial energy of excitation. Beyond a certain energy threshold, when the cubic nonlinearity is present, the system is found to reach energy equipartition and total delocalization. On the other hand, when only the quartic nonlinearity is activated, the system remains localized and away from equipartition at least for the energies and evolution times considered here. However, for large enough energies for all types of nonlinearities we observe chaos. This chaotic behavior is combined with energy delocalization when cubic nonlinearities are present, while the appearance of only quadratic nonlinearity leads to energy localization. Our results reveal a rich dynamical behavior and show differences with the relevant Fermi-Pasta-Ulam-Tsingou model. Our findings pave the way for the study of models relevant to bending (flexural) waves in the presence of nonlinearity and disorder, anticipating different energy transport behaviors.

Designing a phononic crystal with large-size defect to enhance elastic wave energy localization and harvesting

Phononic crystal (PnC) has been proved for its manipulation and amplification of elastic waves. Using this characteristic of PnC to assist energy harvesting has remarkable effect. Generally, defect occurs when unit cell in PnC is replaced by another cell with different geometric or material properties, the output electric power of piezoelectric energy harvesting (PEH) devices will be significantly enhanced. In this study, a cross hole-type PnC-assisted PEH device with a large-size defect is presented by replacing several adjacent multiple cells with other cells. It is found that multiple peak voltages can be created within BG and multimodal energy harvesting can be performed. Compared with the defect mode composed of a small-size defect, energy localization and amplification of the proposed PnC leads to substantially enhancement of harvesting power after tailoring geometric parameters of a PEH device. This work will be expected to design PnC-assisted PEH devices in a reasonable way.

Double defects-induced elastic wave coupling and energy localization in a phononic crystal

This study aims to investigate elastic wave localization that leverages defect band splitting in a phononic crystal with double defects through in-depth analysis of comparison of numerical and experimental results. When more than one defect is created inside a phononic crystal, these defects can interact with each other, resulting in a distinctive physical phenomenon from a single defect case: defect band splitting. For a phononic crystal consisting of circular-hole type unit cells in a thin aluminum plate, under A0 (the lowest antisymmetric) Lamb waves, both numerical simulations and experiments successfully confirm the defect band splitting phenomenon via frequency response functions for the out-of-plane displacement calculated/measured at the double defects within a finite distance. Furthermore, experimental visualization of in-phase and out-of-phase defect mode shapes at each frequency of the split defect bands is achieved and found to be in excellent agreement with the simulated results. Different inter-distance combinations of the double defects reveal that the degree of the defect band splitting decreases with the increasing distance due to weaker coupling between the defects. This work may shed light on engineering applications of a multiple-defect-introduced phononic crystal, including broadband energy harvesting, frequency detectors, and elastic wireless power transfer.

Modeling of supersonic crowdion clusters in FCC lattice: Effect of the interatomic potential

Among a wide variety of point defects, crowdions can be distinguished by their high energy of formation and relatively low migration barriers, which makes them an important agent of mass transfer in lattices subjected to severe plastic deformation, irradiation, etc. It was previously shown that complexes and clusters of crowdions are even more mobile than single interstitials, which opened new mechanisms for the transfer of energy and mass in materials under intense external impacts. One of the most popular and convenient methods for analyzing crowdions is molecular dynamics, where the results can strongly depend on the interatomic potential used in the study. In this work, we compare the characteristics of a crowdion in an fcc lattice obtained using two different interatomic potentials — the pairwise Morse potential and the many-body potential for Al developed by the embedded atom method. It was found that the use of the many-body potential significantly affects the dynamics of crowdion propagation, including the features of atomic collisions, the evolution of energy localization and the propagation path.

Analytical Solutions for Side-branch Impedance Producing Spatial Localization of Acoustic Waves in Ducts with Varying Cross Sections

Analytical mathematical models and solutions for spatial localization of acoustic waves through an impedance discontinuity produced by an intermediate damped side branch are studied in stationary media in ducts with varying cross sections. Three specific geometries, namely, with polynomial, sinusoidal, and exponential longitudinal variations, are investigated. The sound fields inside the ducts are modeled by Webster's horn equation. Traveling-wave solutions are obtained by appropriate transformations. The side-branch impedances required for spatial localization (confinement) of traveling and standing waves are found analytically and verified numerically using three-dimensional finite element analysis. The impact of the longitudinal variation of the duct's cross-sectional area (CSA) on the side-branch impedance is examined. It was found that the required side-branch resistance changes more than the reactance with the variation of the duct CSA. A measure of a traveling wave is defined to quantitatively examine the spatial localization of acoustic waves. It was found that the CSA corrections on the side-branch impedances are important. The results of this study reveal the quantitative relationships between the side-branch impedance and the CSA variations for zero reflection from the impedance discontinuity. The mathematical approach presented is potentially helpful for a design of a full anechoic termination and energy localization in duct systems.

A Phononic Crystal with Differently Configured Double Defects for Broadband Elastic Wave Energy Localization and Harvesting

Several previous studies have been dedicated to incorporating double defect modes of a phononic crystal (PnC) into piezoelectric energy harvesting (PEH) systems to broaden the bandwidth. However, these prior studies are limited to examining an identical configuration of the double defects. Therefore, this paper aims to propose a new design concept for PnCs that examines differently configured double defects for broadband elastic wave energy localization and harvesting. For example, a square-pillar-type unit cell is considered and a defect is considered to be a structure where one piezoelectric patch is bonded to a host square lattice in the absence of a pillar. When the double defects introduced in a PnC are sufficiently distant from each other to implement decoupling behaviors, each defect oscillates like a single independent defect. Here, by differentiating the geometric dimensions of two piezoelectric patches, the defects’ dissimilar equivalent inertia and stiffness contribute to individually manipulating defect bands that correspond to each defect. Hence, with adequately designed piezoelectric patches that consider both the piezoelectric effects on shift patterns of defect bands and the characteristics for the output electric power obtained from a single-defect case, we can successfully localize and harvest the elastic wave energy transferred in broadband frequencies.

Chemistry Under Shock Conditions

Shock loading takes materials from ambient conditions to extreme conditions of temperature and nonhydrostatic stress on picosecond timescales. In molecular materials the fast loading results in temporary nonequilibrium conditions with overheated low-frequency modes and relatively cold, high-frequency, intramolecular modes; coupling the shock front with the material's microstructure and defects results in energy localization in hot spots. These processes can conspire to lead to a material response not observed under quasi-static loads. This review focuses on chemical reactions induced by dynamical loading, the understanding of which requires bringing together materials science, shock physics, and condensed matter chemistry. Recent progress in experiments and simulations holds the key to the answer of long-standing grand challenges with implications for the initiation of detonation and life on Earth. Expected final online publication date for the Annual Review of Materials Science, Volume 51 is August 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.