Marc Serra-Garcia

Granular metamaterials for vibration mitigation

Acoustic metamaterials that allow low-frequency band gaps are interesting for many practical engineering applications, where vibration control and sound insulation are necessary. In most prior studies, the mechanical response of these structures has been described using linear continuum approximations. In this work, we experimentally and theoretically address the formation of low-frequency band gaps in locally resonant granular crystals, where the dynamics of the system is governed by discrete equations. We investigate the quasi-linear behavior of such structures. The analysis shows that a stopband can be introduced at about one octave lower frequency than in materials without local resonances. Broadband and multi-frequency stopband characteristics can also be achieved by strategically tailoring the non-uniform local resonance parameters.

Acoustic Fresnel lenses with extraordinary transmission

We investigate numerically and experimentally highly efficient acoustic lenses based on the principle of extraordinary acoustic transmission. We study circular, flat lenses composed of perforated air channels. The geometry is similar to binary Fresnel lenses, and the lenses exploit several resonance mechanisms to enhance the transmission, such as Fabry–Perot resonances in the channels and cavity resonances on the lens surface. The proposed lenses are able to transmit up to 83% of the incident energy and generate sharp focusing with very high amplification (up to 16 dB experimentally). Furthermore, the resulting lenses are thinner than other designs providing similar performance, making them ideal candidates for application in acoustic imaging and medical diagnostics.

Observation of a phononic quadrupole topological insulator

The modern theory of charge polarization in solids is based on a generalization of Berry’s phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with topological band structures. Although based on the concept of charge polarization, this same theory can also be used to characterize the Bloch bands of neutral bosonic systems such as photonic or phononic crystals. The theory of this quantized polarization has recently been extended from the dipole moment to higher multipole moments. In particular, a two-dimensional quantized quadrupole insulator is predicted to have gapped yet topological one-dimensional edge modes, which stabilize zero-dimensional in-gap corner states. However, such a state of matter has not previously been observed experimentally. Here we report measurements of a phononic quadrupole topological insulator. We experimentally characterize the bulk, edge and corner physics of a mechanical metamaterial (a material with tailored mechanical properties) and find the predicted gapped edge and in-gap corner states. We corroborate our findings by comparing the mechanical properties of a topologically non-trivial system to samples in other phases that are predicted by the quadrupole theory. These topological corner states are an important stepping stone to the experimental realization of topologically protected wave guides in higher dimensions, and thereby open up a new path for the design of metamaterials.

Visco-thermal effects in acoustic metamaterials: from total transmission to total reflection and high absorption

We theoretically and experimentally investigate visco–thermal effects on the acoustic propagation through metamaterials consisting of rigid slabs with subwavelength slits embedded in air. We demonstrate that this unavoidable loss mechanism is not merely a refinement, but that it plays a dominant role in the actual acoustic response of the structure. Specifically, in the case of very narrow slits, the visco–thermal losses avoid completely the excitation of Fabry–Perot resonances, leading to 100% reflection. This is exactly opposite to the perfect transmission predicted in the idealised lossless case. Moreover, for a wide range of geometrical parameters, there exists an optimum slit width at which the energy dissipated in the structure can be as high as 50%. This work provides a clear evidence that visco–thermal effects are necessary to describe realistically the acoustic response of locally resonant metamaterials.

Designing perturbative metamaterials from discrete models

Identifying material geometries that lead to metamaterials with desired functionalities presents a challenge for the field. Discrete, or reduced-order, models provide a concise description of complex phenomena, such as negative refraction, or topological surface states; therefore, the combination of geometric building blocks to replicate discrete models presenting the desired features represents a promising approach. However, there is no reliable way to solve such an inverse problem. Here, we introduce ‘perturbative metamaterials’, a class of metamaterials consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model with individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing two-dimensional elastic metamaterials that realize Veselago lenses, zero-dispersion bands and topological surface phonons. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal and photonic metamaterials composed of weakly interacting unit cells.A perturbative method is proposed for the systematic design of mechanical metamaterials, where each element of the discrete model is associated with individual geometric features of the metamaterial, through the weak interaction between the unit cells.

Mechanical Autonomous Stochastic Heat Engine.

Stochastic heat engines are devices that generate work from random thermal motion using a small number of highly fluctuating degrees of freedom. Proposals for such devices have existed for more than a century and include the Maxwell demon and the Feynman ratchet. Only recently have they been demonstrated experimentally, using, e.g., thermal cycles implemented in optical traps. However, recent experimental demonstrations of classical stochastic heat engines are nonautonomous, since they require an external control system that prescribes a heating and cooling cycle and consume more energy than they produce. We present a heat engine consisting of three coupled mechanical resonators (two ribbons and a cantilever) subject to a stochastic drive. The engine uses geometric nonlinearities in the resonating ribbons to autonomously convert a random excitation into a low-entropy, nonpassive oscillation of the cantilever. The engine presents the anomalous heat transport property of negative thermal conductivity, consisting in the ability to passively transfer energy from a cold reservoir to a hot reservoir.

Tunable, synchronized frequency down-conversion in magnetic lattices with defects

We study frequency conversion in nonlinear mechanical lattices, focusing on a chain of magnets as a model system. We show that, by inserting mass defects at suitable locations, we can introduce localized vibrational modes that nonlinearly couple to extended lattice modes. The nonlinear interaction introduces an energy transfer from the high-frequency localized modes to a low-frequency extended mode. This system is capable of autonomously converting energy between highly tunable input and output frequencies, which need not be related by integer harmonic or subharmonic ratios. It is also capable of obtaining energy from multiple sources at different frequencies with a tunable output phase, due to the defect synchronization provided by the extended mode. Our lattice is a purely mechanical analogue of an opto-mechanical system, where the localized modes play the role of the electromagnetic field and the extended mode plays the role of the mechanical degree of freedom. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

Extreme stiffness tunability through the excitation of nonlinear defect modes.

The incremental stiffness characterizes the variation of a materials force response to a small deformation change. In lattices with noninteracting vibrational modes, the excitation of localized states does not have any effect on material properties, such as the incremental stiffness. We report that, in nonlinear lattices, driving a defect mode introduces changes in the static force-displacement relation of the material. By varying the defect excitation frequency and amplitude, the incremental stiffness can be tuned continuously to arbitrarily large positive or negative values. Furthermore, the defect excitation parameters also determine the displacement region at which the force-displacement relation is being tuned. We demonstrate this phenomenon experimentally in a compressed array of spheres tuning its incremental stiffness from a finite positive value to zero and continuously down to negative infinity.

A metamaterial design method applied to topologically protected mechanical metamaterials

Mass-spring models provide a straightforward way to describe complex dynamic behavior of mechanical systems, such as topologically protected and backscattering-free surface phonons. Such discrete models also provide a means to translate these properties, based on the unique class of electronic materials of topological insulators, to the mechanical domain. This talk will discuss a systematic design process to take such a mass-spring model and implement its functionality directly into a metamaterial. The design method uses combinatorial searches plus gradient-based optimizations to determine the configuration of the metamaterial’s building blocks that replicates the behavior of the target mass-spring model. A key aspect of the design method is the use of “perturbative metamaterials”—i.e., metamaterials with weakly interacting unit cells. The weak coupling enables the design space to be divided into smaller sub-spaces that can be independently tuned, which results in an exponential speed-up of the design pro...