Theoretical and experimental studies of the dynamics and acoustics of forced ordered granular networks
type: CreativeWork
description: Ordered arrays of granular particles (beads) have attracted considerable attention in recent years due to their rich dynamical behaviors and interesting properties. Depending on the ratio of static to dynamic deformations between particles the dynamics of granular media is highly tunable ranging from being strongly nonlinear and non-smooth in the absence of static pre-compression, to reducing to weakly nonlinear and smooth for large static pre-compression. The nonlinearity in uncompressed granular media arises from two sources: First, nonlinear Hertzian interactions, which can be modeled mathematically, between beads in contact, and second, bead separations in the absence of compressive forces between them leading to collisions between adjacent beads. When no applied pre-compression exists there is complete absence of linear acoustics in ordered granular media, which results in zero speed of sound as defined in the sense of linear acoustics through the classical wave equation; thus, these media have been characterized as “sonic vacua”. However, various nonlinear waves can still propagate in these media with energy tunable properties. The first part of this dissertation aims to study the frequency responses of a single homogenous granular chain. We consider a one-dimensional uncompressed granular chain composed of a finite number of identical spherical elastic beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary drive at its left end and has a fixed boundary at its right end. We computationally and experimentally detect time-periodic, strongly nonlinear resonances whereby the particles (beads) of the granular chain respond at integer multiples of the excitation period, and which correspond to local peaks of the maximum transmitted force at the chain’s right, fixed end. In between these resonances we detect local minima of the maximum transmitted forces corresponding to anti-resonances, where chimera sta…
abstract: Ordered arrays of granular particles (beads) have attracted considerable attention in recent years due to their rich dynamical behaviors and interesting properties. Depending on the ratio of static to dynamic deformations between particles the dynamics of granular media is highly tunable ranging from being strongly nonlinear and non-smooth in the absence of static pre-compression, to reducing to weakly nonlinear and smooth for large static pre-compression. The nonlinearity in uncompressed granular media arises from two sources: First, nonlinear Hertzian interactions, which can be modeled mathematically, between beads in contact, and second, bead separations in the absence of compressive forces between them leading to collisions between adjacent beads. When no applied pre-compression exists there is complete absence of linear acoustics in ordered granular media, which results in zero speed of sound as defined in the sense of linear acoustics through the classical wave equation; thus, these media have been characterized as “sonic vacua”. However, various nonlinear waves can still propagate in these media with energy tunable properties. The first part of this dissertation aims to study the frequency responses of a single homogenous granular chain. We consider a one-dimensional uncompressed granular chain composed of a finite number of identical spherical elastic beads with Hertzian interactions. The chain is harmonically excited by an amplitude- and frequency-dependent boundary drive at its left end and has a fixed boundary at its right end. We computationally and experimentally detect time-periodic, strongly nonlinear resonances whereby the particles (beads) of the granular chain respond at integer multiples of the excitation period, and which correspond to local peaks of the maximum transmitted force at the chain’s right, fixed end. In between these resonances we detect local minima of the maximum transmitted forces corresponding to anti-resonances, where chimera sta…
author: Zhang, Yijing
language: en
keywords: Granular media, Acoustic metamaterial
date published: 2017-08-10T19:14:35Z
date modified: 2026-07-22T22:24:32Z
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/2142/97279