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The absorption of sound has great significance in many scientific and engineering applications, from room acoustics to noise mitigation. In this context, porous materials have emerged as a viable solution towards high absorption performance and lightweight designs. However, their performance is somehow limited in the low frequency regime. Inspired by the concept of recursive patterns over multiple length scales typical of many natural materials, here, we propose a hierarchical organization of multilayered porous media and investigate their performance in terms of sound absorption. Two types of designs are investigated: a hierarchical periodic and a hierarchical gradient. In both cases it is found that the introduction of multiple levels of hierarchy allows to simultaneously (i) increase the level of absorption compared to the corresponding bulk block of porous material, along with (ii) a reduction of the quantity of porous material required. Both the cases of normal and oblique incidences are examined. The methodological approach is based on the transfer matrix method, optimization algorithms (metaheuristic Greedy Randomized Adaptive Search Procedure), and finite element calculations. An excellent agreement is found between the analytical and the numerical simulations.

In this paper, we discuss the possibility of achieving tunable topologically protected edge modes through the application of uniaxial deformation in an auxetic metamaterial. The proposed structure consists of a thin slab with oriented cuts in a hexagonal lattice, where topologically protected band gaps are opened by introducing a controlled variation in the cut lengths. Numerical simulations demonstrate the existence of topologically protected and scatter-free wave propagation in the structure at the interface between two sub-domains with modified cells, in distinct frequency ranges. This only occurs in the presence of auxeticity. In addition, exploiting geometrical nonlinearity, the application of a uniaxial strain can be used to close the topological band gaps or to modify their frequency range, i.e., to weaken the localization effects or to shift the frequency at which they occur. The spatial and temporal variation of the applied strain field can thus be used for the dynamic tuning of metamaterial topological waveguiding properties, with applications in mechanical devices for logic operations and computations., Comment: 37 pages, 12 figures

Nature has engineered complex designs to achieve advanced properties and functionalities through evolution, over millions of years. Many organisms have adapted to their living environment producing extremely efficient materials and structures exhibiting optimized mechanical, thermal, optical properties, which current technology is often unable to reproduce. These properties are often achieved using hierarchical structures spanning macro, meso, micro and nanoscales, widely observed in many natural materials like wood, bone, spider silk and sponges. Thus far, bioinspired approaches have been successful in identifying optimized structures in terms of quasi-static mechanical properties, such as strength, toughness, adhesion, but comparatively little work has been done as far as dynamic ones are concerned (e.g. vibration damping, noise insulation, sound amplification, etc.). In particular, relatively limited knowledge currently exists on how hierarchical structure can play a role in the optimization of natural structures, although concurrent length scales no doubt allow to address multiple frequency ranges. Here, we review the main work that has been done in the field of structural optimization for dynamic mechanical properties, highlighting some common traits and strategies in different biological systems. We also discuss the relevance to bioinspired materials, in particular in the field of phononic crystals and metamaterials, and the potential of exploiting natural designs for technological applications.

We report about the effect of an applied external mechanical load on a periodic structure exhibiting band gaps induced by inertial amplification mechanism. If compared to the cases of Bragg scattering and ordinary local resonant metamaterials, we observe here a more remarkable curve shift, modulated through large but fully reversible compression(stretch) of the unit cell, eventually triggering significant (up to two times) enlargement(reduction) of the width of a specific band gap. An important up(down)-shift of some dispersion branches over specific wavenumber values is also observed, showing that this selective variation may lead to negative group velocities over larger(smaller) wavenumber ranges. The possibility for a non-monotone trend of the lower limit of the first BG under the same type of external applied prestrain is found and explained through an analytical model, which unequivocally proves that this behavior derives from the different unit cell effective mass and stiffness variations as the prestrain level increases. The effect of the prestress on the dispersion diagram is investigated through the development of a 2-step calculation method: first, an Updated Lagrangian scheme, including a static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load is derived, and then the Floquet-Bloch decomposition is applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. The results presented herein provide insights in the behavior of band gaps induced by inertial amplification and suggest new opportunities for real-time tunable wave manipulation.

The quest for large and low frequency band gaps is one of the principal objectives pursued in a number of engineering applications, ranging from noise absorption to vibration control, to seismic wave abatement. For this purpose, a plethora of complex architectures (including multi-phase materials) and multi-physics approaches have been proposed in the past, often involving difficulties in their practical realization. To address this issue, in this work we propose an easy-to-manufacture design able to open large, low frequency complete Lamb band gaps exploiting a suitable arrangement of masses and stiffnesses produced by cavities in a monolithic material. The performance of the designed structure is evaluated by numerical simulations and confirmed by Scanning Laser Doppler Vibrometer (SLDV) measurements on an isotropic polyvinyl chloride plate in which a square ring region of cross-like cavities is fabricated. The full wave field reconstruction clearly confirms the ability of even a limited number of unit cell rows of the proposed design to efficiently attenuate Lamb waves. In addition, numerical simulations show that the structure allows to shift of the central frequency of the BG through geometrical modifications. The design may be of interest for applications in which large BGs at low frequencies are required.

The investigation of topologically protected waves in classical media has opened unique opportunities to achieve exotic properties like one-way phonon transport, protection from backscattering and immunity to imperfections. Contrary to acoustic and electromagnetic domains, their observation in elastic solids has so far been elusive due to the presence of both shear and longitudinal modes and their modal conversion at interfaces and free surfaces. Here we report the experimental observation of topologically protected helical edge waves in elastic media. The considered structure consists of an elastic plate patterned according to a Kagome architecture with an accidental degeneracy of two Dirac cones induced by drilling through holes. The careful breaking of symmetries couples the corresponding elastic modes which effectively emulates spin orbital coupling in the quantum spin Hall effect. The results shed light on the topological properties of the proposed plate waveguide and opens avenues for the practical realization of compact, passive and cost-effective elastic topological waveguides.

Attenuating low-frequency sound remains a challenge, despite many advances in this direction. Recently developed acoustic metamaterials enable efficient subwavelength wave manipulation and attenuation due to exotic effects such as unusually high reflectivity, negative refraction or cloaking. In particular, labyrinthine acoustic metamaterials can provide broadband sound reduction and exhibit extremely high effective refractive index values due to their characteristic topological architecture. In this paper, we design a novel labyrinthine metamaterial with hybrid characteristics compared to previously proposed structures, by exploiting a spider web-inspired configuration. The developed metamaterial structure is characterized by additional tunability of the frequencies at which band gaps or negative group velocity modes occur, thus enabling versatility in the functionalities of the resulting structures. Time transient simulations demonstrate the effectiveness of the proposed metamaterials in manipulating wave fields in terms of transmission/reflection coefficients, amplitude attenuation and time delay properties in broadband frequency ranges. Results could find applications in the development of practical lightweight acoustic shielding structures with enhanced broadband wave-reflecting performance., Comment: 25 pages, 7 figures, submitted