arXiv subjects

Stefano Gonella

Publications and source records attributed to Stefano Gonella.

At least 37 records · Page 2Linked to original sources

arXiv2021

Wavenumber-space band clipping in nonlinear periodic structures

In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as a initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally-resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.

nlin.PS↗

arXiv2021

Tunable bandgaps and symmetry breaking in magneto-mechanical metastructures inspired by multi-layer 2D materials

In this Letter, we introduce a paradigm to realize magneto-mechanical metastructures inspired by multi-layer 2D materials, such as graphene bilayers. The metastructures are intended to capture two aspects of their nanoscale counterparts. One is the multi-layer geometry, which is implemented by stacking hexagonal lattice sheets. The other is the landscape of weak inter-layer forces, which is mimicked by the interactions between pairs of magnets located at corresponding lattice sites on adjacent layers. We illustrate the potential of this paradigm through a three-layer prototype. The two rigid outer lattices serve as control layers, while the thin inner layer is free to experience flexural motion under the confining action of the magnetic forces exchanged with the outer ones, thus behaving as a lattice on elastic foundation. The inner layer is free to rotate relatively to the others, giving rise to a rich spectrum of inter-layer interaction patterns. Our objective is to determine how the dynamical response can be tuned by changing the twist angle between the layers. Specifically, we demonstrate experimentally that switching between different stacking patterns has profound consequences on the phonon landscape, opening and closing bandgaps in different frequency regimes.

cond-mat.mtrl-sci↗

arXiv2021

Symmetry of the phonon landscape across the duality boundary of twisted kagomes lattices

In this work, we investigate the symmetry of the phonon landscape of twisted kagome lattices across their duality boundary. The study is inspired by recent work by Fruchart et al. [Nature, 577, 2020], who specialized the notion of duality to the mechanistic problem of kagome lattices and linked it to the existence of duality transformations between configurations that are symmetrically located across a critical transition point in configuration space. Our first goal is to elucidate how the existence of matching phonon spectra between dual configurations manifest in terms of observable wavefield characteristics. To this end, we explore the possibility to aggregate dual kagome configurations into bi-domain lattices that are geometrically heterogeneous but retain a mechanically homogeneous response. Our second objective is to extend the analysis to structural lattices of beams, which are representative of realistic cellular metamaterials. We show that, in this case, the symmetry of the phonon landscape across the duality boundary is broken, implying that the conditions for dual behavior do not merely depend on the geometry, but also on the dominant mechanisms of the cell, suggesting a dichotomy between geometric and functional duality.

cond-mat.mtrl-sci↗

arXiv2020

Soft topological lattice wheels

We investigate the large deformation and extreme load-management capabilities of a soft topologically polarized kagome lattice mapped to a cylindrical domain through the problem of a lattice wheel rolling on an irregular surface. We test the surface-lattice interaction experimentally by subjecting a 3D-printed topological lattice wheel prototype to localized and distributed boundary loads. This investigation reveals a dichotomy in the force transfer between the two loading scenarios, whereby localized loads are absorbed with limited stress penetration into the bulk and small force transfer to the wheel axle, compared to distributed loads. Through numerical simulations, we compare the lattice wheel against a baseline solid wheel to highlight the unique stress management opportunities offered by the lattice configuration. These findings promote the design of rolling objects enabled by topological mechanics, in which a surplus of softness, activated by local asperities, can coexist with a globally stiff response to distributed loads that ensures satisfactory load-bearing capabilities.

cond-mat.mtrl-sci↗

arXiv2020

Dynamics of interacting particle systems: Modeling implications of the repulsive interactions and experiments on magnetic prototypes

In this work, we investigate the dynamics of interacting particle systems subjected to repulsive forces, such as lattices of magnetized particles. To this end, we first develop a general model capable of capturing the complete dynamical behavior of interacting particle systems governed by arbitrary potentials. The model elucidates the important role played by the static repulsive forces exchanged between particles in the initial equilibrium configuration, which is distilled and mathematically captured by a dedicated component of the stiffness matrix. The implications of the model are then examined through the simple illustrative example of a magnetic particle oscillator, by which we show that the effect associated with the initial static forces is germane to two- or higher-dimensional particle systems and vanishes for 1D chains. In the context of wave propagation, we show that this type of effect manifests as modal-selective corrections of the dispersion relation of 2D repulsive lattices. To corroborate these findings, we perform laser vibrometry experiments on a lattice prototype consisting of a triangular grid of magnets supported by an elastic foundation of thin pillars. The tests unequivocally confirm the emergence of distinctive dispersive regimes in quantitative accordance to the model.

physics.app-ph↗

arXiv2020

Nonlinear harmonic generation in two-dimensional lattices of repulsive magnets

In this Letter, we provide experimental evidence of nonlinear wave propagation in a triangular lattice of repulsive magnets supported by an elastic foundation of thin pillars and we interpret all the individual features of the nonlinear wavefield through the lens of a phonon band calculation that precisely accounts for the inter-particle repulsive forces. We confirm the co-existence of two spectrally distinct components (homogeneous and forced) in the wave response that is induced via second harmonic generation (SHG), a well-known effect of quadratic nonlinearity (here embedded in the magnetic interaction). We show that the modal and spatial characteristics of the second harmonic components are complementary to those exhibited by the fundamental harmonic. This endows the lattice with a functionality enrichment capability, whereby additional modes and directivity patterns can be triggered and tuned by merely increasing the amplitude of excitation.

nlin.PS↗

arXiv2020

Bandgap widening by disorder in rainbow metamaterials

Stubbed plates, i.e., thin elastic sheets endowed with pillar-like resonators, display subwavelength, locally-resonant bandgaps that are primarily controlled by the intrinsic resonance properties of the pillars. In this work, we experimentally study the bandgap response of a tunable heterogeneous plate endowed with reconfigurable families of pillars. We demonstrate that, under certain circumstances, both the spectrum of resonant frequencies of the pillars and their spatial arrangement influence the filtering characteristics of the system. Specifically, both spatially graded and disordered arrangements result in bandgap widening. Moreover, the spectral range over which attenuation is achieved with random arrangements is on average wider than the one observed with graded configurations.

cond-mat.mtrl-sci↗

arXiv2019

Valley-Hall In-Plane Edge States as Building Blocks for Elastodynamic Logic Circuits

In this work, we investigate theoretically and demonstrate experimentally the existence of valley-Hall edge states in the in-plane dynamics of honeycomb lattices with bi-valued strut thickness. We exploit these states to achieve non-trivial waveguiding of optical modes that is immune to backscattering from sharp corners. We also present how different types of interfaces can be combined into multi-branch junctions to form complex waveguide paths and realize a variety of structural logic designs with unconventional wave transport capabilities. We illustrate this potential with two applications. The first is a direction-selective energy-splitting waveguide tree featuring a pronounced asymmetric wave transport behavior. The second is an internal waveguide loop along which the energy can be temporarily trapped and periodically released, effectively working as a signal delayer. The modal complexity of in-plane elasticity has important consequences on the regime of manifestation of the edge states, as the availability of viable total bandgaps is shifted to higher frequencies compared to the out-of-plane counterpart problem. It also poses additional experimental challenges, associated with proper acquisition and deciphering of the in-plane modes, the solution of which requires a systematic use of in-plane laser vibrometry.

physics.app-ph↗

arXiv2019

Switchable phonon diodes using nonlinear topological Maxwell lattices

Recent progress in topological mechanics have revealed a family of Maxwell lattices that exhibit topologically protected floppy edge modes. These modes lead to a strongly asymmetric elastic wave response. In this paper, we show how topological Maxwell lattices can be used to realize non-reciprocal transmission of elastic waves. Our design leverages the asymmetry associated with the availability of topological floppy edge modes and the geometric nonlinearity built in the mechanical systems response to achieve the desired non-reciprocal behavior, which can be further turned into strongly one-way phonon transport via the addition of on-site pinning potentials. Moreover, we show that the non-reciprocal wave transmission can be switched on and off via topological phase transitions, paving the way to the design of cellular metamaterials that can serve as tunable topologically protected phonon diodes.

cond-mat.soft↗

arXiv2019

Doubly-nonlinear waveguides with self-switching functionality selection capabilities

In this article, we investigate the effects of the interplay between quadratic and cubic nonlinearities on the propagation of elastic waves in periodic waveguides. Through this framework, we unveil an array of wave control strategies that are intrinsically available in the response of doubly-nonlinear systems and we infer some basic design principles for tunable elastic metamaterials. The objective is to simultaneously account for two sources of nonlinearity that are responsible for distinct and complementary phenomena and whose effects are therefore typically discussed separately in the literature. Our study explicitly targets the intertwined effects that the two types of nonlinearity exert on each other, which modify the way in which their respective signatures are observed in the dynamic response. Through two illustrative examples we show how the dispersion correction caused by cubic nonlinearity can be used as an internal switch, or mode selector, capable of tuning on/off certain high-frequency response features that are generated through quadratic mechanisms.

nlin.PS↗

arXiv2018

Improved Support Recovery Guarantees for the Group Lasso With Applications to Structural Health Monitoring

This paper considers the problem of estimating an unknown high dimensional signal from noisy linear measurements, {when} the signal is assumed to possess a \emph{group-sparse} structure in a {known,} fixed dictionary. We consider signals generated according to a natural probabilistic model, and establish new conditions under which the set of indices of the non-zero groups of the signal (called the group-level support) may be accurately estimated via the group Lasso. Our results strengthen existing coherence-based analyses that exhibit the well-known "square root" bottleneck, allowing for the number of recoverable nonzero groups to be nearly as large as the total number of groups. We also establish a sufficient recovery condition relating the number of nonzero groups and the signal to noise ratio (quantified in terms of the ratio of the squared Euclidean norms of nonzero groups and the variance of the random additive {measurement} noise), and validate this trend empirically. Finally, we examine the implications of our results in the context of a structural health monitoring application, where the group Lasso approach facilitates demixing of a propagating acoustic wavefield, acquired on the material surface by a scanning laser Doppler vibrometer, into antithetical components, one of which indicates the locations of internal material defects.

cs.IT↗

arXiv2018

Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies

Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic laser-assisted experimental characterization of topological kagome lattices, aimed at elucidating their in-plane phononic and topological characteristics. We specifically explore the continuum elasticity limit, which is established when the ideal hinges that appear in the theoretical models are replaced by ligaments capable of supporting bending deformation, as observed for instance in realistic physical lattices. We reveal how the zero-energy floppy edge modes predicted for ideal configurations morph into finite-frequency phonon modes that localize at the edges. By probing the lattices with carefully designed excitation signals, we are able to extract and characterize all the features of a complex low-frequency acoustic regime in which bulk modes and topological edge modes overlap and entangle in response. The experiments provide unequivocal evidence of the existence of strong asymmetric wave transport regimes at finite frequencies.

cond-mat.mtrl-sci↗

arXiv2018

Pathway towards programmable wave anisotropy in cellular metamaterials

In this work, we provide a proof-of-concept experimental demonstration of the wave control capabilities of cellular metamaterials endowed with populations of tunable electromechanical resonators. Each independently tunable resonator comprises a piezoelectric patch and a resistor-inductor shunt, and its resonant frequency can be seamlessly re-programmed without interfering with the cellular structure's default properties. We show that, by strategically placing the resonators in the lattice domain and by deliberately activating only selected subsets of them, chosen to conform to the directional features of the beamed wave response, it is possible to override the inherent wave anisotropy of the cellular medium. The outcome is the establishment of tunable spatial patterns of energy distillation resulting in a non-symmetric correction of the wavefields.

physics.app-ph↗

arXiv2017

Wave control through soft microstructural curling: bandgap shifting, reconfigurable anisotropy and switchable chirality

In this work, we discuss and numerically validate a strategy to attain reversible macroscopic changes in the wave propagation characteristics of cellular metamaterials with soft microstructures. The proposed cellular architecture is characterized by unit cells featuring auxiliary populations of symmetrically-distributed smart cantilevers stemming from the nodal locations. Through an external stimulus (the application of an electric field), we induce extreme, localized, reversible curling deformation of the cantilevers---a shape modification which does not affect the overall shape, stiffness and load bearing capability of the structure. By carefully engineering the spatial pattern of straight (non activated) and curled (activated) cantilevers, we can induce several profound modifications of the phononic characteristics of the structure: generation and/or shifting of total and partial bandgaps, cell symmetry relaxation (which implies reconfigurable wave beaming), and chirality switching. While in this work we discuss the specific case of composite cantilevers with a PDMS core and active layers of electrostrictive terpolymer P(VDF-TrFE-CTFE), the strategy can be extended to other smart materials (such as dielectric elastomers or shape-memory polymers).

cond-mat.soft↗

arXiv2016

Experimental Evidence of Directivity-Enhancing Mechanisms in Nonlinear Lattices

In this letter, we experimentally investigate the directional characteristics of propagating, finite-amplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly-generated higher harmonics. To this end, we subject a thin, periodically perforated sheet to out-of-plane harmonic excitations, and we design a systematic measurement and data processing routine that leverages the full-wavefield reconstruction capabilities of a laser vibrometer to precisely delineate the effects of nonlinearity. We demonstrate experimentally that the interplay of dispersion, nonlinearity, and modal complexity which is involved in the generation and propagation of higher harmonics gives rise to secondary wave packets with characteristics that conform to the dispersion relation of the corresponding linear structure. Furthermore, these nonlinearly generated wave features display modal and directional characteristics that are complementary to those exhibited by the fundamental harmonic, thus resulting in an augmentation of the functionality landscape of the lattice. These results provide proof of concept for the possibility to engineer the nonlinear wave response of mechanical metamaterials through a geometric and topological design of the unit cell.

nlin.PS↗

arXiv2016

Nonlinear Waves in Lattice Materials: Adaptively Augmented Directivity and Functionality Enhancement by Modal Mixing

The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite-deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation - an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.

nlin.PS↗

arXiv2016

Manipulating waves by distilling frequencies: a tunable shunt-enabled rainbow trap

In this work, we propose and test a strategy for tunable, broadband wave attenuation in electromechanical waveguides with shunted piezoelectric inclusions. Our strategy is built upon the vast pre-existing literature on vibration attenuation and bandgap generation in structures featuring periodic arrays of piezo patches, but distinguishes itself for several key features. First, we demystify the idea that periodicity is a requirement for wave attenuation and bandgap formation. We further embrace the idea of "organized disorder" by tuning the circuits as to resonate at distinct neighboring frequencies. In doing so, we create a tunable "rainbow trap" [Tsakmakidis et al. Nature 450, 397-401 (2007)] capable of attenuating waves with broadband characteristics, by "distilling" (sequentially) seven frequencies from a traveling wavepacket. Finally, we devote considerable attention to the implications in terms of packet distortion of the spectral manipulation introduced by shunting. This work is also meant to serve as a didactic tool for those approaching the field of shunted piezoelectrics, and attempts to provide a different perspective, with abundant details, on how to successfully design an experimental setup involving resistive-inductive shunts.

cond-mat.mtrl-sci↗

arXiv2016

Manipulating waves with LEGO$^{\circledR}$ bricks: A versatile experimental platform for metamaterial architectures

In this letter, we discuss a versatile, fully-reconfigurable experimental platform for the investigation of phononic phenomena in metamaterial architectures. The approach revolves around the use of 3D laser vibrometry to reconstruct global and local wavefield features in specimens obtained through simple arrangements of LEGO$^{\circledR}$ bricks on a thin baseplate. The agility by which it is possible to reconfigure the brick patterns into a nearly endless spectrum of topologies makes this an effective approach for rapid experimental proof of concept, as well as a powerful didactic tool, in the arena of phononic crystals and metamaterials engineering. We use our platform to provide a compelling visual illustration of important spatial wave manipulation effects (waveguiding and seismic isolation), and to elucidate fundamental dichotomies between Bragg-based and locally resonant bandgap mechanisms.

cond-mat.mtrl-sci↗