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