142 research outputs found
Time-modulated inerters as building blocks for nonreciprocal mechanical devices
In this work, we discuss the realization of mechanical devices with
non-reciprocal attributes enabled by inertia-amplifying, time-modulated
mechanisms. Our fundamental building-block features a mass, connected to a
fixed ground through a spring and to a moving base through a mechanism-based
inerter. Through analytical derivations and numerical simulations, we provide
details on the nonlinear dynamics of such system. We demonstrate that providing
a time modulation to the inerter's base produces two additions on the dynamics
of the main spring-mass oscillator: i) an effective time-modulated mass term,
and ii) a time varying force term; both quantities are functions of the
modulating frequency. With specific choices of parameters, the
modulation-induced force term -- that represents one of the main drawbacks in
most experimental realizations of purely time-modulated systems -- vanishes and
we are left with an effective time-varying mass. We then illustrate that this
building block can be leveraged to realize non-reciprocal wave manipulation
devices, and concentrate on a non-reciprocal beam-like waveguide. The simple
design and the clean performance of our system makes it an attractive candidate
for the realization of fully mechanical non-reciprocal devices
Compliant morphing structures from twisted bulk metallic glass ribbons
In this work, we investigate the use of pre-twisted metallic ribbons as
building blocks for shape-changing structures. We manufacture these elements by
twisting initially flat ribbons about their (lengthwise) centroidal axis into a
helicoidal geometry, then thermoforming them to make this configuration a
stress-free reference state. The helicoidal shape allows the ribbon to have
preferred bending directions that vary throughout its length. These bending
directions serve as compliant joints and enable several deployed and stowed
configurations that are unachievable without pre-twist, provided that
compaction does not induce material failure. We fabricate these ribbons using a
bulk metallic glass (BMG), for its exceptional elasticity and thermoforming
attributes. Combining numerical simulations, an analytical model based on shell
theory and torsional experiments, we analyze the finite-twisting mechanics of
various ribbon geometries. We find that, in ribbons with undulated edges, the
twisting deformations can be better localized onto desired regions prior to
thermoforming. Finally, we join together multiple ribbons to create deployable
systems. Our work proposes a framework for creating fully metallic, yet
compliant structures that may find application as elements for space structures
and compliant robots
Reconfigurable wave manipulation in smart cellular solids
University of Minnesota Ph.D. dissertation. July 2017. Major: Civil Engineering. Advisor: Stefano Gonella. 1 computer file (PDF); vii, 114 pages.Metamaterials are man-made materials designed to display properties which are not attainable by conventional materials. They owe their behavior to their mesoscale architecture, which often revolves around the periodic arrangement of a repetitive volume element, or unit cell. A particularly prominent application of metamaterials is in the context of wave control, where they have been used as mechanical filters, energy steering devices, and optical and acoustic cloaks. This thesis work tackles a few open problems within this fertile and fast-growing field. Specifically, one of our main aims is to unveil the relationship between the symmetry of the unit cell of a given periodic medium and the symmetry of its wave response, and to provide a mechanistic rationale for the generation of anisotropic wave patterns in specific frequency ranges. We then propose two strategies to modify these patterns in the context of periodic cellular solids (lattice structures). The first strategy, based on the concept of cell symmetry relaxation, relies on a symmetry-driven microstructural design of the unit cell, in which the geometric and material characteristics of certain microstructural features are modulated to modify the symmetry landscape of the cell. The second one, that we named anisotropy overriding, is based on the interplay between the intrinsically anisotropic wave patterns of the medium and the corrective action of a small number of strategically-placed resonators. We also propose tunable implementations of these strategies, which are achieved by incorporating into the periodic architectures smart material inserts (e.g., shunted piezoelectric patches and curlable dielectric elastomers) which are activated using external non-mechanical stimuli. The resulting wave manipulation effects are illustrated through a series of numerical simulations and experimental tests
Modeling planar kirigami metamaterials as generalized elastic continua
Planar kirigami metamaterials dramatically change their shape through a
coordinated motion of nearly rigid panels and flexible slits. Here, we study a
model system for mechanism-based planar kirigami featuring periodic patterns of
quadrilateral panels and rhombi slits, with the goal of predicting their
engineering scale response to a broad range of loads. We develop a generalized
continuum model based on the kirigami's effective (cell-averaged) deformation,
along with its slit actuation and gradients thereof. The model accounts for
three sources of elasticity: a strong preference for the effective fields to
match those of a local mechanism, inter-panel stresses arising from gradients
in slit actuation, and distributed hinge bending. We provide a finite element
formulation of this model and implement it using the commercial software
Abaqus. Simulations of the model agree with experiments across designs and
loading conditions.Comment: 15 pages, 8 figure
Surface wave non-reciprocity via time-modulated metamaterials
We investigate how Rayleigh waves interact with modulated resonators located
on the free surface of a semi-infinite elastic medium. We begin by studying the
dynamics of a single resonator with time-modulated stiffness. In particular, we
evaluate the accuracy of an analytical approximation of the resonator response
and identify the parameter ranges in which its behavior remains stable. Then,
we develop an analytical model to describe the interaction between surface
waves and an array of resonators with spatio-temporally modulated stiffness. By
combining our analytical models with full-scale numerical simulations, we
demonstrate that spatio-temporal stiffness modulation of this elastic
metasurface leads to the emergence of non-reciprocal features in the Rayleigh
wave spectrum. Specifically, we show how the frequency content of a propagating
signal can be filtered and converted when traveling through the modulated
medium, and illustrate how surface-to-bulk wave conversion plays a role in
these phenomena. Throughout this article, we indicate bounds of modulation
parameters for which our theory is reliable, thus providing guidelines for
future experimental studies on the topic
Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors
In this work, we construct an effective continuum model for architected
sheets that are composed of bulky tiles connected by slender elastic joints.
Due to their mesostructure, these sheets feature quasi-mechanisms -- low-energy
local kinematic modes that are strongly favored over other deformations. In
sheets with non-uniform mesostructure, kinematic incompatibilities arise
between neighboring regions, causing out-of-plane buckling. The effective
continuum model is based on a geometric analysis of the sheets' unit cells and
their energetically favorable modes of deformation. Its major feature is the
construction of a strain energy that penalizes deviations from these preferred
modes of deformation. The effect of non-periodicity is entirely described
through the use of spatially varying geometric parameters in the model. Our
simulations capture the out-of-plane buckling that occurs in non-periodic
specimens and show good agreement with experiments. While we only consider one
class of quasi-mechanisms, our modeling approach could be applied to a diverse
set of shape-morphing systems that are of interest to the mechanics community
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