190 research outputs found
Dynamics of a Monolayer of Microspheres on an Elastic Substrate
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 closed-form 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 to a discrete model of a monolayer on a rigid substrate.
While the effective medium model does not account for discrete lattice effects
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 discrete monolayer
adhered to an elastic substrate can be found using a combination of the results
presented for the discrete and effective medium descriptions. This model is
potentially scalable for use with both micro- and macroscale systems, and
offers the prospect of experimentally extracting contact stiffnesses from
measurements of acoustic dispersion
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
Exploring the Past: A Retrospective Look at the Experiences of Young Men in High School Physical Education Classes
High school physical education classes aim to provide young men with the competence and confidence needed to lead a physically active lifestyle (Borghese, 2019; Tanaka et al., 2018). As well, physical education is recognized as a significant contributor to the daily accumulation of moderate to vigorous physical activity among young men (Tanaka et al., 2018). However, a considerable gap exists in the literature regarding what specific factors influence young men to participate during their physical education classes. Using a retrospective, qualitative description study, this research project explored the previous high school physical education experiences of 10 male-identifying students at the University of Saskatchewan. Using two rounds of semi-structured, individual interviews, each participant’s previous physical education experiences were investigated at length. The findings from these individual interviews can be understood through three themes: Us and Them, The Physical Education Teacher: “Him and His Football Boys” and Physical Cultural Capital. Woven throughout these three themes, the findings suggest that several key factors play a role in determining a young man’s participation and engagement in physical education. These key factors include competitiveness, participation in community hockey or on the school football team, relationships with the physical education teacher and accruement of physical cultural capital. The findings of this study support previous research, identifying physical cultural capital as a factor that affects engagement in physical education (Jachyra, 2014). As there is a paucity of research regarding young mens’ experiences with participation in physical education, this study aimed to add relevant information to a topic that lacks sufficient research
Wrinkles Riding Waves in Soft Layered Materials
The formation of periodic wrinkles in soft layered materials due to
mechanical instabilities is prevalent in nature and has been proposed for use
in multiple applications. However, such phenomena have been explored
predominantly in quasi-static settings. In this work, we measure the dynamics
of soft elastomeric blocks with stiff surface films subjected to high-speed
impact, and observe wrinkles forming along with, and riding upon, waves
propagating through the system. We analyze our measurements with
large-deformation, nonlinear visco-hyperelastic Finite Element simulations
coupled to an analytical wrinkling model. The comparison between the measured
and simulated dynamics shows good agreement, and suggests that inertia and
viscoelasticity play an important role. This work encourages future studies of
the dynamics of surface instabilities in soft materials, including
large-deformation, highly nonlinear morphologies, and may have applications to
areas including impact mitigation, soft electronics, and the dynamics of soft
sandwich composites
Longitudinal Eigenvibration of Multilayer Colloidal Crystals and the Effect of Nanoscale Contact Bridges
Longitudinal contact-based vibrations of colloidal crystals with a controlled
layer thickness are studied. These crystals consist of 390 nm diameter
polystyrene spheres arranged into close packed, ordered lattices with a
thickness of one to twelve layers. Using laser ultrasonics, eigenmodes of the
crystals that have out-of-plane motion are excited. The particle-substrate and
effective interlayer contact stiffnesses in the colloidal crystals are
extracted using a discrete, coupled oscillator model. Extracted stiffnesses are
correlated with scanning electron microscope images of the contacts and atomic
force microscope characterization of the substrate surface topography after
removal of the spheres. Solid bridges of nanometric thickness are found to
drastically alter the stiffness of the contacts, and their presence is found to
be dependent on the self-assembly process. Measurements of the eigenmode
quality factors suggest that energy leakage into the substrate plays a role for
low frequency modes but is overcome by disorder- or material-induced losses at
higher frequencies. These findings help further the understanding of the
contact mechanics, and the effects of disorder in three-dimensional micro- and
nano-particulate systems, and open new avenues to engineer new types of micro-
and nanostructured materials with wave tailoring functionalities via control of
the adhesive contact properties
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