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We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry within the unit cell. Examples for discrete one and two-dimensional lattices elucidate the concept and illustrate parallels with the quantum valley Hall effect. The concept is implemented on an elastic plate featuring an array of resonators arranged according to a hexagonal topology. The resulting continuous structures have non-trivial bandgaps supporting edge waves at the interface between two media with different topological invariants. The topological properties of the considered configurations are predicted by unit cell and finite strip dispersion analyses. Numerical simulations demonstrate edge wave propagation for excitation at frequencies belonging to the bulk bandgaps. The considered plate configurations define a framework for the implementation of topological concepts on continuous elastic structures of potential engineering relevance.

This work investigates the amplitude-dependent dynamics of a locally resonant metamaterial beam with bistable attachments. The concept that was previously demonstrated for a discrete chain is extended to a continuous system, and the enhancement in vibration attenuation bandwidth is investigated through a cantilever beam under base excitation. The analysis approach combines the harmonic balance method and time-domain numerical integration to capture periodic and aperiodic responses for up-sweep and down-sweep harmonic excitation. The bistable attachments are shown to exhibit linear intrawell, nonlinear intrawell and nonlinear interwell oscillations for low, moderate, and high base acceleration levels. As a result, the metastructure leverages linear locally resonant bandgap under low excitation intensity, and nonlinear wideband attenuation due to chaotic vibrations of the bistable attachments under high excitation intensity. This is first demonstrated through frequency sweep numerical simulations for a broad range of excitation amplitudes. Experimental validations are then presented for a base-excited cantilever beam hosting seven magnetoelastic beam attachments. For moderate-to-high amplitude excitation levels, the interwell oscillations of the attachments produce an attenuation frequency range that is 350% wider than the corresponding linear locally resonant bandgap (observed for low-amplitude excitation levels), yielding the suppression of modes outside the bandgap with increased excitation intensity.

The law of reciprocity in acoustics and elastodynamics codifies a relation of symmetry between action and reaction in fluids and solids. In its simplest form, it states that the frequency-response functions between any two material points remain the same after swapping source and receiver, regardless of the presence of inhomogeneities and losses. As such, reciprocity has enabled numerous applications that make use of acoustic and elastic wave propagation. A recent change in paradigm has prompted us to see reciprocity under a new light: as an obstruction to the realization of wave-bearing media in which the source and receiver are not interchangeable. Such materials may enable the creation of devices such as acoustic one-way mirrors, isolators and topological insulators. Here, we review how reciprocity breaks down in materials with momentum bias, structured space-dependent and time-dependent constitutive properties, and constitutive nonlinearity, and report on recent advances in the modelling and fabrication of these materials, as well as on experiments demonstrating nonreciprocal acoustic and elastic wave propagation therein. The success of these efforts holds promise to enable robust, unidirectional acoustic and elastic wave-steering capabilities that exceed what is currently possible in conventional materials, metamaterials or phononic crystals. Nonreciprocal acoustic and elastic wave propagation may enable the creation of devices such as acoustic one-way mirrors, isolators and topological insulators. This Review presents advances in the creation of materials that break reciprocity and realize robust, unidirectional acoustic and elastic wave steering.

We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.

In this report, we design a one-dimensional elastic phononic crystal (PC) comprised of an Aluminum beam with periodically arranged cross-sections to study the inversion of bulk bands due to the change of topological phases. As the geometric parameters of the unit cell varies, the second bulk band closes and reopens forming a topological transition point. This phenomenon is confirmed for both longitudinal waves and bending waves. By constructing a structural system formed by two PCs with different topological phases, for the first time, we experimentally demonstrate the existence of interface mode within the bulk band gap as a result of topological transition for both longitudinal and bending modes in elastic systems, although for bending modes, additional conditions have to be met in order to have the interface mode due to the dispersive nature of the bending waves in uniform media compared to the longitudinal waves.

We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground springs at locations determined by projecting from a circle onto an underlying periodic system. A family of periodic and quasiperiodic structures is obtained by smoothly varying a parameter defining such projection. Numerical simulations show the existence of vibration modes that first localize at a boundary, and then migrate into the bulk as the projection parameter is varied. Explicit expressions predicting the change in the density of states of the bulk define topological invariants that quantify the number of modes spanning a gap of a finite structure. We further demonstrate how modulating the phase of the ground springs distribution causes the topological states to undergo an edge-to-edge transition. The considered configurations and topological studies provide a framework for inducing localized modes in continuous elastic structural components through globally spanning, deterministic perturbations of periodic patterns defined by the considered projection operations.

Topological physics has been driving exciting progress in the area of condensed matter physics, with findings that have recently spilled over into the field of metamaterials research inspiring the design of structured materials that can govern in new ways the flow of light and sound. While so far these advances have been driven by fundamental curiosity-driven explorations, without a focused interest on their technological implications, opportunities to translate these findings into applied research have started to emerge, in particular in the context of sound control. Our team has been leading a highly collaborative research effort on advancing the field of topological acoustics, dubbed ‘New Frontiers of Sound’ and connecting it to technological opportunities for computing, communications, energy and sensing. In this comment, we outline our vision towards the future of topological sound, and its translation towards industry-relevant functionalities and operations based on extreme control of acoustic and phononic waves.

Additive manufacturing has become a fundamental tool to fabricate and experimentally investigate mechanical metamaterials and phononic crystals. However, this manufacturing process produces spatially correlated variability that breaks the translational periodicity, which might compromise the wave propagation performance of metamaterials. We demonstrate that the vibration attenuation profile is strictly related to the spatial profile of the variability, and that there exists an optimal disorder degree below which the attenuation bandwidth widens; for high disorder levels, the band gap mistuning annihilates the overall attenuation. The variability also induces a spatially variant locally resonant band gap that progressively slow down the group velocity until an almost zero value, giving rise to wave trapping effect near the lower band gap boundary. Inspired by this wave trapping phenomenon, a rainbow metamaterial with linear spatial-frequency trapping is also proposed, which have potential applications in energy harvesting, spatial wave filtering and non-destructive evaluation at low frequency. This report provides a deeper understanding of the differences between numerical simulations using nominal designed properties and experimental analysis of metamaterials constructed in 3D printing. These analysis and results may extend to phononic crystals and other periodic systems to investigate their wave and dynamic performance as well as robustness under variability.

Manipulation of micro/nano particles has been well studied and demonstrated by optical, electromagnetic, and acoustic approaches, or their combinations. Manipulation of internal structure of droplet/particle is rarely explored and remains challenging due to its complicated nature. Here we demonstrated the manipulation of internal structure of disk-in-sphere endoskeletal droplets using acoustic wave. We developed a model to investigate the physical mechanisms behind this interesting phenomenon. Theoretical analysis of the acoustic interactions indicated that these assembly dynamics arise from a balance of the primary and secondary radiation forces. Additionally, the disk orientation was found to change with acoustic driving frequency, which allowed on-demand, reversible adjustment of the disk orientations with respect to the substrate. This dynamic behavior leads to unique reversible arrangements of the endoskeletal droplets and their internal architecture, which may provide an avenue for directed assembly of novel hierarchical colloidal architectures and intracellular organelles or intra-organoid structures. Endoskeletal droplets are a class of complex colloids containing a solid internal phase cast within a liquid emulsion droplet. Here, authors show acoustic manipulation of solid disks inside liquid droplets whose orientation can be externally controlled with the frequency.

We investigate the spectral properties of one-dimensional spatially modulated nonlinear phononic lattices, and their evolution as a function of amplitude. In the linear regime, the stiffness modulations define a family of periodic and quasiperiodic lattices whose bandgaps host topological edge states localized at the boundaries of finite domains. With cubic nonlinearities, we show that edge states whose eigenvalue branch remains within the gap as amplitude increases remain localized, and therefore appear to be robust with respect to amplitude. In contrast, edge states whose corresponding branch approaches the bulk bands experience de-localization transitions. These transitions are predicted through continuation studies on the linear eigenmodes as a function of amplitude, and are confirmed by direct time domain simulations on finite lattices. Through our predictions, we also observe a series of amplitude-induced localization transitions as the bulk modes detach from the nonlinear bulk bands and become discrete breathers that are localized in one or more regions of the domain. Remarkably, the predicted transitions are independent of the size of the finite lattice, and exist for both periodic and quasiperiodic lattices. These results highlight the co-existence of topological edge states and discrete breathers in nonlinear modulated lattices. Their interplay may be exploited for amplitude-induced eigenstate transitions, for the assessment of the robustness of localized states, and as a strategy to induce discrete breathers through amplitude tuning.