Strongly nonlinear dynamics and acoustics of coupled granular sonic vacua: theoretical and experimental studies
type: CreativeWork
description: Passive control of energy flow by means of trapping, redirection and scattering has been the subject of considerable attention in recent years. The use of ordered granular media is a promising candidate for such designs. Ordered granular media are ordered aggregates, where neighboring particles (or granules) interact elastically in a highly nonlinear fashion. These highly discontinuous media have strongly nonlinear behavior owing to Hertzian interactions between granules in compression, and separations – collisions of the same granules in the absence of compression. Depending on the ratio of static to dynamic interparticle deformations and displacements, the nonlinear dynamics of ordered granular media is highly adaptive, ranging from being essentially nonlinear (even non-linearizable) and non-smooth (in the absence of static pre-compression), to being weekly nonlinear and smooth or even linear (with high static pre-compression). Moreover, such interplay between strongly nonlinear and weakly nonlinear dynamics may occur in different phases of the same dynamic response of a granular medium subject to a given external excitation. In this dissertation, we aim to analyze the strongly nonlinear dynamics of coupled ordered granular media and investigate interesting response regimes such as, passive wave redirection / redistribution and targeted energy transfer (TET). These studies are performed using numerical computations, analytical calculations, and experimental tests. In particular, we consider weakly coupled granular chains with or without on-site potentials, as well as two-dimensional granular networks with regularly placed intruders that act as effective coupling elements. Unlike previous studies of weakly coupled oscillatory chains, the dynamical systems considered herein incorporate both non-smooth effects due to possible separations between interacting neighboring beads (granules), as well as strongly nonlinear inter-particle Hertzian interactions. We show that …
abstract: Passive control of energy flow by means of trapping, redirection and scattering has been the subject of considerable attention in recent years. The use of ordered granular media is a promising candidate for such designs. Ordered granular media are ordered aggregates, where neighboring particles (or granules) interact elastically in a highly nonlinear fashion. These highly discontinuous media have strongly nonlinear behavior owing to Hertzian interactions between granules in compression, and separations – collisions of the same granules in the absence of compression. Depending on the ratio of static to dynamic interparticle deformations and displacements, the nonlinear dynamics of ordered granular media is highly adaptive, ranging from being essentially nonlinear (even non-linearizable) and non-smooth (in the absence of static pre-compression), to being weekly nonlinear and smooth or even linear (with high static pre-compression). Moreover, such interplay between strongly nonlinear and weakly nonlinear dynamics may occur in different phases of the same dynamic response of a granular medium subject to a given external excitation. In this dissertation, we aim to analyze the strongly nonlinear dynamics of coupled ordered granular media and investigate interesting response regimes such as, passive wave redirection / redistribution and targeted energy transfer (TET). These studies are performed using numerical computations, analytical calculations, and experimental tests. In particular, we consider weakly coupled granular chains with or without on-site potentials, as well as two-dimensional granular networks with regularly placed intruders that act as effective coupling elements. Unlike previous studies of weakly coupled oscillatory chains, the dynamical systems considered herein incorporate both non-smooth effects due to possible separations between interacting neighboring beads (granules), as well as strongly nonlinear inter-particle Hertzian interactions. We show that …
author: Hasan, Md Arif
language: en
keywords: Granular Media, Solitary Waves, Standing Breathers, Traveling Breathers, Wave Equipartition, Targeted Energy Transfer, Landau–Zener Tunneling, Acoustic Metamaterial, Acoustic Stop- And Pass-Bands
date published: 2014-09-16T17:23:41Z
date modified: 2026-07-22T22:25:40Z
provider: University of Illinois - Urbana-Champaign
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Illinois at Urbana-Champaign

PropertyValue
property ID: Handle
value: http://hdl.handle.net/2142/50546