Stefano Gonella

Tunable directivity in metamaterials with reconfigurable cell symmetry

We introduce a strategy to attain reconfigurable, highly focused, subwavelength wave patterns in cellular metamaterials via electromechanical tuning of their microstructures. The metamaterial cells feature a population of auxiliary microstructural elements instrumented with piezoelectric patches connected to negative capacitance shunting circuits. By tuning the circuital characteristics of selected subsets of shunts, we relax the symmetry of the cell material property landscape, thus affecting the global directivity and enabling a plethora of wave manipulation capabilities. The acoustic reconfiguration is decoupled from other mechanical functions and is carried out without affecting the shape or the static properties of the host cellular structure.

Low-frequency spatial wave manipulation via phononic crystals with relaxed cell symmetry

Phononic crystals enjoy unique wave manipulation capabilities enabled by their periodic topologies. On one hand, they feature frequency-dependent directivity, which allows directional propagation of selected modes even at low frequencies. However, the stellar nature of the propagation patterns and the inability to induce single-beam focusing represent significant limitations of this functionality. On the other hand, one can realize waveguides by defecting the periodic structure of a crystal operating in bandgap mode along some desired path. Waveguides of this type are only activated in the relatively high and narrow frequency bands corresponding to total bandgaps, which limits their potential technological applications. In this work, we introduce a class of phononic crystals with relaxed cell symmetry and we exploit symmetry relaxation of a population of auxiliary microstructural elements to achieve spatial manipulation of elastic waves at very low frequencies, in the range of existence of the acoustic mo...

Manipulating waves with LEGO® 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® 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.

Noisy Matrix Completion Under Sparse Factor Models

This paper examines a general class of noisy matrix completion tasks, where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is on settings where the matrix to be estimated is well-approximated by a product of two (a priori unknown) matrices, one of which is sparse. Such structural models-referred to here as sparse factor models-have been widely used, for example, in subspace clustering applications, as well as in contemporary sparse modeling and dictionary learning tasks. Our main theoretical contributions are estimation error bounds for sparsity-regularized maximum likelihood estimators for the problems of this form, which are applicable to a number of different observation noise or corruption models. Several specific implications are examined, including scenarios where observations are corrupted by additive Gaussian noise or additive heavier-tailed (Laplace) noise, Poisson-distributed observations, and highly quantized (e.g., 1 b) observations. We also propose a simple algorithmic approach based on the alternating direction method of multipliers for these tasks, and provide experimental evidence to support our error analyses.

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).

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.

Wave Propagation and Band-Gap Characteristics of Chiral Lattices

Plane wave propagation in a chiral lattice is investigated through the application of Blochs theorem. Two-dimensional dispersion relations are estimated and analyzed to illustrate peculiar properties of chiral or non-centrosymmetric configurations and investigate the directional behavior of wave propagation for varying geometric parameters. Special attention is devoted to the determination of phase and group wave velocities. Considerations based upon the analysis of velocity plots are compared with results obtained from dispersion curves to further validate the directional behavior of the proposed lattice. Finally, The relation of directionality with frequency of the traveling waves is discussed.

Multicell Homogenization of One-Dimensional Periodic Structures

Much attention has been recently devoted to the application of homogenization methods for the prediction of the dynamic behavior of periodic domains. One of the most popular techniques employs the Fourier transform in space in conjunction with Taylor series expansions to approximate the behavior of structures in the low frequency/long wavelength regime. The technique is quite effective, but suffers from two major drawbacks. First, the order of the Taylor expansion, and the corresponding frequency range of approximation, is limited by the resulting order of the continuum equations and by the number of boundary conditions, which may be imposed in accordance with the physical constraints on the system. Second, the approximation at low frequencies does not allow capturing bandgap characteristics of the periodic domain. An attempt at overcoming the latter can be made by applying the Fourier series expansion to a macrocell spanning two (or more) irreducible unit cells of the periodic medium. This multicell approach allows the simultaneous approximation of low frequency and high frequency dynamic behavior and provides the capability of analyzing the structural response in the vicinity of the lowest bandgap. The method is illustrated through examples on simple one-dimensional structures to demonstrate its effectiveness and its potentials for application to complex one-dimensional and two-dimensional configurations.

Error bounds for maximum likelihood matrix completion under sparse factor models

This paper examines a general class of matrix completion tasks where entry wise observations of the matrix are subject to random noise or corruption. Our particular focus here is on settings where the matrix to be estimated follows a sparse factor model, in the sense that it may be expressed as the product of two matrices, one of which is sparse. We analyze the performance of a sparsity-penalized maximum likelihood approach to such problems to provide a general-purpose estimation result applicable to any of a number of noise/corruption models, and describe its implications in two stylized scenarios - one characterized by additive Gaussian noise, and the other by highly-quantized one-bit observations. We also provide some supporting empirical evidence to validate our theoretical claims in the Gaussian setting.

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 ...