Ultrasonic metamaterials with negative modulus

Stretchable Ultrasound Metalens for Biomedical Zoom Imaging and Bone Quality Assessment with Subwavelength Resolution

Ultrasound imaging is extensively used in biomedical science and clinical practice. Imaging resolution and tunability of imaging plane are key performance indicators, but both remain challenging to be improved due to the longer wavelength compared with light and the lack of zoom lens for ultrasound. Here, the ultrasound zoom imaging based on a stretchable planar metalens that simultaneously achieves the subwavelength imaging resolution and dynamic control of the imaging plane is reported. The proposed zoom imaging ultrasonography enables precise bone fracture diagnosis and comprehensive osteoporosis assessment. Millimeter-scale microarchitectures of the cortical bones at different depths can be selectively imaged with a 0.6-wavelength resolution. The morphological features of bone fractures, including the shape, size and position, are accurately detected. Based on the extracted ultrasound information of cancellous bones with healthy matrix, osteopenia and osteoporosis, a multi-index osteoporosis evaluation method is developed. Furthermore, it provides additional biological information in aspects of bone elasticity and attenuation to access the comprehensive osteoporosis assessment. The soft metalens also features flexibility and biocompatibility for preferable applications on wearable devices. This work provides a strategy for the development of high-resolution ultrasound biomedical zoom imaging and comprehensive bone quality diagnosis system.

Inherent Temporal Metamaterials with Unique Time-Varying Stiffness and Damping

Time-varying metamaterials offer new degrees of freedom for wave manipulation and enable applications unattainable with conventional materials. In these metamaterials, the pattern of temporal inhomogeneity is crucial for effective wave control. However, existing studies have only demonstrated abrupt changes in properties within a limited range or time modulation following simple patterns. This study presents the design, construction, and characterization of a novel temporal elastic metamaterial with complex time-varying constitutive parameters induced by self-reconfigurable virtual resonators (VRs). These VRs, achieved by simulating the resonating behavior of mechanical resonators in digital space, function as virtualized meta-atoms. The autonomously time-varying VRs cause significant temporal variations in both the stiffness and loss factor of the metamaterial. By programming the time-domain behavior of the VRs, the metamaterial's constitutive parameters can be modulated according to desired periodic or aperiodic patterns. The proposed time-varying metamaterial has demonstrated capabilities in shaping the amplitudes and frequency spectra of waves in the time domain. This work not only facilitates the development of materials with sophisticated time-varying properties but also opens new avenues for low-frequency signal processing in future communication systems.

An efficient multiscale method for subwavelength transient analysis of acoustic metamaterials

A reduced-order homogenization framework is proposed, providing a macro-scale-enriched continuum model for locally resonant acoustic metamaterials operating in the subwavelength regime, for both time and frequency domain analyses. The homogenized continuum has a non-standard constitutive model, capturing a metamaterial behaviour such as negative effective bulk modulus, negative effective density and Willis coupling. A suitable reduced space is constructed based on the unit cell response in a steady-state regime and the local resonance regime. A frequency domain numerical example demonstrates the efficiency and suitability of the proposed framework.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Ultra-broadband illusion acoustics for space and time camouflages

Invisibility cloaks that can suppress wave scattering by objects have attracted a tremendous amount of interest in the past two decades. In comparison to prior methods that were severely limited by narrow bandwidths, here we present a practical strategy to suppress sound scattering across an ultra-broad spectrum by leveraging illusion metamaterials. Consisting of a collection of subwavelength tunnels with precisely crafted internal structures, this illusion metamaterial has the ability to guide acoustic waves around the obstacles and accurately recreate the incoming wavefront on the exit surface. Remarkably, two ultra-broadband illusionary effects are produced, disappearing space and time shift. Sound scatterings are removed at all frequencies below a limit determined by the tunnel width, as confirmed by full-wave simulations and acoustic experiments. Our strategy represents a universal approach to solve the key bottleneck of bandwidth limitation in the field of cloaking in transmission, and establishes a metamaterial platform that enables the long-desired ultra-broadband sound manipulation such as acoustic camouflage and reverberation control, opening up exciting new possibilities in practical applications.

Current developments in elastic and acoustic metamaterials science

The concept of metamaterial recently emerged as a new frontier of scientific research, encompassing physics, materials science and engineering. In a broad sense, a metamaterial indicates an engineered material with exotic properties not found in nature, obtained by appropriate architecture either at macro-scale or at micro-/nano-scales. The architecture of metamaterials can be tailored to open unforeseen opportunities for mechanical and acoustic applications, as demonstrated by an impressive and increasing number of studies. Building on this knowledge, this theme issue aims to gather cutting-edge theoretical, computational and experimental studies on elastic and acoustic metamaterials, with the purpose of offering a wide perspective on recent achievements and future challenges. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Piezoelectric Microacoustic Metamaterial Filters

We present the first microacoustic metamaterial filters (MMFs). The bandpass of the reported MMFs is not generated by coupling, electrically or mechanically, various acoustic resonances; instead, it originates from the passbands and stopbands of a chain of three acoustic metamaterial (AM) structures. These structures form an AM transmission line (AMTL) and two AM reflectors (AMRs), respectively. Two single metal strips serve as input and output transducers with a wideband frequency response. Since MMFs do not rely on resonators, they do not require high-resolution trimming or mass-loading steps to accurately tune the resonance frequency difference between various microacoustic resonant devices. These steps often involve finely controlling the thickness of a device layer, with resolutions that can be as low as a few Angstroms when building GHz filters. The acoustic bandwidth of MMFs is mostly determined by geometrical and mechanical parameters of their AM structures. MMFs necessitate external circuit components for impedance matching, in contrast to the existing microacoustic filters that often employ circuit components only to eliminate ripples within their passband. We have designed and constructed the first MMFs from a 400-nm-thick scandium-doped aluminum nitride (AlScN) film using a 30% scandium-doping concentration. These devices operate in the radio frequency (RF) range. We validated these devices' performance through finite-element modeling (FEM) simulations and through measurements of a set of fabricated devices. When matched with ideal circuit components, the built MMFs exhibit filter responses with a center frequency in the ultrahigh-frequency range, a fractional bandwidth (FBW) of ~2.54%, a loss of ~4.9 dB, an in-band group delay between 70 ± 25 ns, and a temperature coefficient of frequency (TCF) of ~22.2 ppm/° C.

Methods of Manipulation of Acoustic Radiation Using Metamaterials with a Focus on Polymers: Design and Mechanism Insights

The manipulation of acoustic waves is becoming increasingly crucial in research and practical applications. The coordinate transformation methods and acoustic metamaterials represent two significant areas of study that offer innovative strategies for precise acoustic wave control. This review highlights the applications of these methods in acoustic wave manipulation and examines their synergistic effects. We present the fundamental concepts of the coordinate transformation methods and their primary techniques for modulating electromagnetic and acoustic waves. Following this, we deeply study the principle of acoustic metamaterials, with particular emphasis on the superior acoustic properties of polymers. Moreover, the polymers have the characteristics of design flexibility and a light weight, which shows significant advantages in the preparation of acoustic metamaterials. The current research on the manipulation of various acoustic characteristics is reviewed. Furthermore, the paper discusses the combined use of the coordinate transformation methods and polymer acoustic metamaterials, emphasizing their complementary nature. Finally, this article envisions future research directions and challenges in acoustic wave manipulation, considering further technological progress and polymers' application potential. These efforts aim to unlock new possibilities and foster innovative ideas in the field.

Broadband acoustic illusion coating based on thin conformal metasurface

Acoustic metasurface with rationally distributed phase manipulating characteristic provides a promising platform to reshape the wavefront of scattering wave. Such acoustic illusion carpet suffers from limitation of narrow bandwidth and relatively large volume to contain the object to be hidden. Here, we propose and experimentally demonstrate broadband conformal acoustic illusion coatings composed of subwavelength-thick metacells that are designed by two types of modified Helmholtz resonators with 2π reflection phase. By deliberate design of reflection phase distributions of illusion coating, the reflected wavefront can be reshaped between trapezoid and triangles and vice versa. Furthermore, an enlarged illusion is obtained by this methodology. More importantly, the illusion behaviors are verified both numerically and experimentally from 3000 Hz to 4500 Hz, resulting in relatively broad bandwidth up to 40.5%, which is definitely of extreme importance for potential applications.

Advanced Ultrasound Energy Transfer Technologies using Metamaterial Structures

Wireless energy transfer (WET) based on ultrasound-driven generators with enormous beneficial functions, is technologically in progress by the valuation of ultrasonic metamaterials (UMMs) in science and engineering domains. Indeed, novel metamaterial structures can develop the efficiency of mechanical and physical features of ultrasound energy receivers (US-ETs), including ultrasound-driven piezoelectric and triboelectric nanogenerators (US-PENGs and US-TENGs) for advantageous applications. This review article first summarizes the fundamentals, classification, and design engineering of UMMs after introducing ultrasound energy for WET technology. In addition to addressing using UMMs, the topical progress of innovative UMMs in US-ETs is conceptually presented. Moreover, the advanced approaches of metamaterials are reported in the categorized applications of US-PENGs and US-TENGs. Finally, some current perspectives and encounters of UMMs in US-ETs are offered. With this objective in mind, this review explores the potential revolution of reliable integrated energy transfer systems through the transformation of metamaterials into ultrasound-driven active mediums for generators.

Bubbles enable volumetric negative compressibility in metastable elastocapillary systems

Although coveted in applications, few materials expand when subject to compression or contract under decompression, i.e., exhibit negative compressibility. A key step to achieve such counterintuitive behaviour is the destabilisations of (meta)stable equilibria of the constituents. Here, we propose a simple strategy to obtain negative compressibility exploiting capillary forces both to precompress the elastic material and to release such precompression by a threshold phenomenon - the reversible formation of a bubble in a hydrophobic flexible cavity. We demonstrate that the solid part of such metastable elastocapillary systems displays negative compressibility across different scales: hydrophobic microporous materials, proteins, and millimetre-sized laminae. This concept is applicable to fields such as porous materials, biomolecules, sensors and may be easily extended to create unexpected material susceptibilities.

Nonreciprocal field transformation with active acoustic metasurfaces

Field transformation, as an extension of the transformation optics, provides a unique means for nonreciprocal wave manipulation, while the experimental realization remains a substantial challenge as it requires stringent material parameters of the metamaterials, e.g., purely nonreciprocal bianisotropic parameters. Here, we develop and demonstrate a nonreciprocal field transformation in a two-dimensional acoustic system, using an active metasurface that can independently control all constitutive parameters and achieve purely nonreciprocal Willis coupling. The field-transforming metasurface enables tailor-made field distribution manipulation, achieving localized field amplification by a predetermined ratio. The metasurface demonstrates the self-adaptive capability to various excitation conditions and can be extended to other geometric shapes. The metasurface also achieves nonreciprocal wave propagation for internal and external excitations, demonstrating a one-way acoustic device. The nonreciprocal field transformation not only extends the framework of the transformation theory for nonreciprocal wave manipulation but also holds great potential in applications such as ultrasensitive sensors and nonreciprocal communication.

Studies on Dual Helmholtz Resonators and Asymmetric Waveguides for Ventilated Soundproofing

Achieving the simultaneity of ventilation and soundproofing is a significant challenge in applied acoustics. Ventilated soundproofing relies on the interplay between local resonance and nonlocal coupling of acoustic waves within a sub-wavelength structure. However, previously studied structures possess limited types of fundamental resonators and lack modifications from the basic arrangement. These constraints often force the specified position of each attenuation peak and low absorption performance. Here, we suggest the in-duct-type sound barrier with dual Helmholtz resonators, which are positioned around the symmetry-breaking waveguides. The numerical simulations for curated dimensions and scattered fields show the aperiodic migrations and effective amplifications of the two absorptive domains. Collaborating with the subsequent reflective domains, the designed structure holds two effective attenuation bands under the first Fabry-Pérot resonance frequency. This study would serve as a valuable example for understanding the local and non-local behaviors of sub-wavelength resonating structures. Additionally, it could be applied in selective noise absorption and reflection more flexibly.

On enhancing the noise-reduction performance of the acoustic lined duct utilizing the phase-modulating metasurface

This work proposes a noise-reduction structure that integrates phase-modulating metasurface (PMM) with acoustic liners (ALs) to enhance the narrow band absorption performance of a duct with relatively small length-diameter ratio. The PMM manipulates the wavefront by introducing different transmission phase shifts based on an array of Helmholtz resonators, so that the spinning wave within the duct can be generated. Compared with the plane wave, the generated spinning wave has a lower group velocity, which results in a greater traveling distance over the ALs in the duct. The optimization design is performed to determine the final structural parameters of the PMM, which is based on the predictions of the amplitude and phase shift of the acoustic wave at the outlet of the PMM using the theory of passive phased array. With the manipulation of the PMM, the incident plane wave is modulated into a spinning wave, and then enters into the acoustic liner duct (ALD), whose structural parameters are optimized by maximizing the transmission loss using the mode-matching technique. Finally, the noise-reduction performance of this combined structure is evaluated by numerical simulations in the presence of grazing flow. The results demonstrate that, compared with the traditional ALD, the proposed structure exhibits a significant increase in transmission loss within the considered frequency band, especially near the peak frequency of the narrow band noise.

Superwavelength self-healing of spoof surface sonic Airy-Talbot waves

Self-imaging phenomena for nonperiodic waves along a parabolic trajectory encompass both the Talbot effect and the accelerating Airy beams. Beyond the ability to guide waves along a bent trajectory, the self-imaging component offers invaluable advantages to lensless imaging comprising periodic repetition of planar field distributions. In order to circumvent thermoviscous and diffraction effects, we structure subwavelength resonators in an acoustically impenetrable surface supporting spoof surface acoustic waves (SSAWs) to provide highly confined Airy-Talbot effect, extending Talbot distances along the propagation path and compressing subwavelength lobes in the perpendicular direction. From a linear array of loudspeakers, we judiciously control the amplitude and phase of the SSAWs above the structured surface and quantitatively evaluate the self-healing performance of the Airy-Talbot effect by demonstrating how the distinctive scattering patterns remain largely unaffected against superwavelength obstacles. Furthermore, we introduce a new mechanism utilizing subwavelength Airy beam as a coding/decoding degree of freedom for acoustic communication with high information density comprising robust transport of encoded signals.

Recent Progress in Resonant Acoustic Metasurfaces

Acoustic metasurfaces, as two-dimensional acoustic metamaterials, are a current research topic for their sub-wavelength thickness and excellent acoustic wave manipulation. They hold significant promise in noise reduction and isolation, cloaking, camouflage, acoustic imaging, and focusing. Resonant structural units are utilized to construct acoustic metasurfaces with the unique advantage of controlling large wavelengths within a small size. In this paper, the recent research progresses of the resonant metasurfaces are reviewed, covering the design mechanisms and advances of structural units, the classification and application of the resonant metasurfaces, and the tunable metasurfaces. Finally, research interest in this field is predicted in future.

Broadband sound absorption based on impedance decoupling and modulation mechanisms

In sound absorbers, acoustic resistance and reactance are usually coupled together and affect each other, which brings difficulties to impedance matching. An impedance decoupling method is proposed to make acoustic resistance and acoustic reactance vary independently. For the same thickness and perforation rate, acoustic reactance of the perforated panel with tube bundles (PPTBs) varies with the diameter of the tube, but acoustic resistance remains constant. Theoretical and simulated results show that a PPTB absorptive unit can exhibit resonance modes with varying damping states through impedance decoupling. It is found that through well-modulation, the PPTB unit in a slightly over-damped state cannot only maintain high sound absorption coefficients, but also expand the absorption peak bandwidth. Utilizing the mechanism of impedance decoupling, a broadband absorber is designed and evaluated by comprising the PPTB and microperforated panel (MPP). Measurement results indicate that it possesses an average absorption coefficient of 85% spanning more than a 3-octave bandwidth from 160 Hz to 1400 Hz with a deep sub-wavelength thickness. The impedance decoupling method helps to implement sound absorbers with highly efficient low-frequency broadband absorption.

Principles of progressive slow-sound and critical coupling condition in broadband sonic black hole absorber

Recent advances in sonic black hole (SBH) provide new opportunities for controlling sound waves and designing wave manipulation devices. SBH is a device that consists of partitions with gradually decreasing inner radii inserted into an acoustic duct. Several studies have reported that SBH can achieve a broadband sound absorption coefficient close to 1, avoiding the issue of alternating high and low absorption coefficients observed in traditional sound absorbers. However, the fundamental mechanisms and principles behind this behavior are not yet fully understood. This study aims to investigate the detailed sound absorption mechanisms of SBH, including the progressive slow-sound effect and the critical coupling condition that leads to broadband sound absorption. To achieve this goal, an analytical model based on the effective medium approach is developed to investigate the layer-by-layer retardation in sound propagation. The sound absorption coefficient is then determined based on the surface impedance calculation. The effective medium analysis reveals that SBH enables a unique condition to progressively decelerate wave propagation across its layers. As a result, the critical coupling condition becomes more easily established with smoothly increasing SBH partitions and more discretised layers, as elucidated by the complex frequency analysis results. The physical insights gained from this study reveal the distinctive features of SBH compared to classical sound absorbers, paving the way for its engineering applications.

An ultra-broadband solar absorber based on α-GST/Fe metamaterials from visible light to mid-infrared

In this paper, we proposed an ultra-broadband and high absorption rate absorber based on Fe materials. The proposed absorber consists of a rectangle pillar, two rings, a SiO2 film, a Ge2Sb2Te5(GST) planar cavity, an Fe mirror, and a SiO2 substrate. The average absorption reaches 98.45% in the range of 400-4597 nm. We investigate and analyze the electric field distributions. The analysis of the physical mechanism behind the broadband absorption effect reveals that it is driven by excited surface plasmons. Furthermore, the absorber can maintain high absorption efficiency under a large incident angle. The geometrical symmetric structure possesses polarization insensitivity properties. The proposed structure allows for certain manufacturing errors, which improves the feasibility of the actual manufacture. Then, we investigate the effect of different materials on absorption. Finally, we study the matching degree between the energy absorption spectrum and the standard solar spectrum under AM 1.5. The results reveal that the energy absorption spectrum matches well with the standard solar spectrum under AM 1.5 over the full range of 400 to 6000 nm. In contrast, energy loss can be negligible. The absorber possesses ultra-broadband perfect absorption, a high absorption rate, and a simple structure which is easy to manufacture. It has tremendous application potential in many areas, such as solar energy capture, thermal photovoltaics, terminal imaging, and other optoelectronic devices.

Tunable Helmholtz Resonators Using Multiple Necks

One of the uses of Helmholtz resonators is as sound absorbers for room acoustic applications, especially for the low frequency range. Their efficiency is centered around their resonance frequency which mainly depends on elements of their geometry such as the resonator volume and neck dimensions. Incorporating additional necks on the body of a Helmholtz resonator (depending on whether they are open or closed) has been found to alter the resulting resonance frequency. For this study, tunable Helmholtz resonators to multiple resonance frequencies, are proposed and investigated utilizing additional necks. The resonance frequencies of various multi-neck Helmholtz resonators are first modeled with the use of the finite element method (FEM), then calculated with the use of an analytical approach and the results of the two approaches are finally compared. The results of this study show that Helmholtz resonators with multiple resonances at desired frequencies are achievable with the use of additional necks, while FEM and analytical methods can be used for the estimation of the resonance frequencies. Analytical and FEM approach results show a good agreement in cases of small number of additional necks, while the increasing differences in cases of higher neck additions, were attributed to the change in effective length of the necks as demonstrated by FEM. The proposed approach can be useful for tunable sound absorbers for room acoustics applications according to the needs of a space. Also, this approach can be applied in cases of additional tunable air resonances of acoustic instruments (e.g., string instruments).

Extending the Linearity of AlScN Contour-Mode Resonators Through Acoustic Metamaterials-Based Reflectors

This work describes the implementation of acoustic metamaterials (AMs) made of a forest of rods at the sides of a suspended aluminum scandium nitride (AlScN) contour-mode resonator (CMR) to increase its power handling without causing degradations of its electromechanical performance. The increase in usable anchoring perimeter with respect to conventional CMR designs, enabled by the adoption of two AM-based lateral anchors, permits to achieve improved heat conduction from the resonator's active region to the substrate. Furthermore, thanks to such AM-based lateral anchors' unique acoustic dispersion features, the attained increase of anchored perimeter does not cause any degradations of the CMR's electromechanical performance, even leading to a ~15% improvement in the measured quality factor. Finally, we experimentally show that using our AM-based lateral anchors leads to a more linear CMR's electrical response, which is enabled by a 32% reduction of its Duffing nonlinear coefficient with respect to the corresponding value attained by a conventional CMR design that uses fully etched lateral sides.

Non-reciprocal and non-Newtonian mechanical metamaterials

Non-Newtonian liquids are characterized by stress and velocity-dependent dynamical response. In elasticity, and in particular, in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton's second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using three-dimensional printing at the centimetric scale (with fused deposition modeling) and at the micrometric scale (with two-photon lithography). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response.

Sound attenuation enhancement of acoustic meta-atoms via coupling

Arrangements of acoustic meta-atoms, better known as acoustic metamaterials, are commonly applied in acoustic cloaking, for the attenuation of acoustic fields or for acoustic focusing. A precise design of single meta-atoms is required for these purposes. Understanding the details of their interaction allows improvement of the collective performance of the meta-atoms as a system, for example, in sound attenuation. Destructive interference of their scattered fields, for example, can be mitigated by adjusting the coupling or tuning of individual meta-atoms. Comprehensive numerical studies of various configurations of a resonator pair show that the coupling can lead to degenerate modes at periodic distances between the resonators. We show how the resonators' separation and relative orientation influence the coupling and thereby tunes the sound attenuation. The simulation results are supported by experiments using a two-dimensional parallel-plate waveguide. It is shown that coupling parameters like distance, orientation, detuning, and radiation loss provide additional degrees of freedom for efficient acoustic meta-atom tuning to achieve unprecedented interactions with excellent sound attenuation properties.

Extreme Spatial Dispersion in Nonlocally Resonant Elastic Metamaterials

To date, the vast majority of architected materials have leveraged two physical principles to control wave behavior, namely, Bragg interference and local resonances. Here, we describe a third path: structures that accommodate a finite number of delocalized zero-energy modes, leading to anomalous dispersion cones that nucleate from extreme spatial dispersion at 0 Hz. We explain how to design such zero-energy modes in the context of elasticity and show that many of the landmark wave properties of metamaterials can also be induced at an extremely subwavelength scale by the associated anomalous cones, without suffering from the same bandwidth limitations. We then validate our theory through a combination of simulations and experiments. Finally, we present an inverse design method to produce anomalous cones at desired locations in k space.

3D Printed Graphene-Based Metamaterials: Guesting Multi-Functionality in One Gain

Advanced functional materials with fascinating properties and extended structural design have greatly broadened their applications. Metamaterials, exhibiting unprecedented physical properties (mechanical, electromagnetic, acoustic, etc.), are considered frontiers of physics, material science, and engineering. With the emerging 3D printing technology, the manufacturing of metamaterials becomes much more convenient. Graphene, due to its superior properties such as large surface area, superior electrical/thermal conductivity, and outstanding mechanical properties, shows promising applications to add multi-functionality into existing metamaterials for various applications. In this review, the aim is to outline the latest developments and applications of 3D printed graphene-based metamaterials. The structure design of different types of metamaterials and the fabrication strategies for 3D printed graphene-based materials are first reviewed. Then the representative explorations of 3D printed graphene-based metamaterials and multi-functionality that can be introduced with such a combination are further discussed. Subsequently, challenges and opportunities are provided, seeking to point out future directions of 3D printed graphene-based metamaterials.

Refraction, beam splitting and dispersion of GHz surface acoustic waves by a phononic crystal

We exploit a time-resolved ultrafast optical technique to study the propagation of point-excited surface acoustic waves on a microscopic two-dimensional phononic crystal in the form of a square lattice of holes in a silicon substrate. Constant-frequency images and the dispersion relation are extracted, and the latter measured in detail in the region around the phononic band gap. Mode conversion and refraction at the interface between the phononic crystal and surrounding non-structured silicon substrate is studied at constant frequencies. Symmetric phonon beam splitting, for example, is shown to lead to a striking Maltese-cross pattern when phonons exit a square region of phononic crystal excited near its center.

Architected material with independently tunable mass, damping, and stiffness via multi-stability and kinematic amplification

We report on a class of architected material lattices that exploit multi-stability and kinematic amplification to independently adjust the local effective mass, damping, and stiffness properties, thereby realizing congruent alterations to the acoustic dispersion response post-fabrication. The fundamental structural tuning element permits a broad range in the effective property space; moreover, its particular design carries the benefit of tuning without altering the original size/shape of the emerging structure. The relation between the tuning element geometry and the achieved variability in effective properties is explored. Bloch's theorem facilitates the dynamic analysis of representative one- and two-dimensional (1D/2D) systems, revealing, e.g., bandgap formation, migration, and closure and positive/negative metadamping in accordance with the tuning element configuration. To demonstrate a utility, we improvise a waveguide by appropriately patterning the tuning element configuration within a 2D system. We believe that the proposed strategy offers a new way to expand the range of performance and functionality of architected materials for elastodynamics.

Hybrid fractal acoustic metamaterials for low-frequency sound absorber based on cross mixed micro-perforated panel mounted over the fractals structure cavity

The proposed work enumerates a hybrid thin, deep-subwavelength (2 cm) acoustic metamaterials acting as a completely new type of sound absorber, showing multiple broadband sound absorption effects. Based on the fractal distribution of Helmholtz resonator (HRs) structures, integrated with careful design and construct hybrid cross micro-perforated panel (CMPP) that demonstrate broad banding approximately one-octave low-frequency sound absorption behavior. To determine the sound absorption coefficient of this novel type of metamaterial, the equivalent impedance model for the fractal cavity and the micro-perforated Maa's model for CMPP are both used. We validate these novel material designs through numerical, theoretical, and experimental data. It is demonstrated that the material design possesses superior sound absorption which is primarily due to the frictional losses of the structure imposed on acoustic wave energy. The peaks of different sound absorption phenomena show tunability by adjusting the geometric parameters of the fractal structures like cavity thickness 't', cross perforation diameter of micro perforated panel, etc. The fractal structures and their perforation panel are optimized dimensionally for maximum broadband sound absorption which is estimated numerically. This new kind of fractals cavity integrated with CMPP acoustic metamaterial has many applications as in multiple functional materials with broad-band absorption behavior etc.

A solution to the biophysical fractionation of extracellular vesicles: Acoustic Nanoscale Separation via Wave-pillar Excitation Resonance (ANSWER)

High-precision isolation of small extracellular vesicles (sEVs) from biofluids is essential toward developing next-generation liquid biopsies and regenerative therapies. However, current methods of sEV separation require specialized equipment and time-consuming protocols and have difficulties producing highly pure subpopulations of sEVs. Here, we present Acoustic Nanoscale Separation via Wave-pillar Excitation Resonance (ANSWER), which allows single-step, rapid (<10 min), high-purity (>96% small exosomes, >80% exomeres) fractionation of sEV subpopulations from biofluids without the need for any sample preprocessing. Particles are iteratively deflected in a size-selective manner via an excitation resonance. This previously unidentified phenomenon generates patterns of virtual, tunable, pillar-like acoustic field in a fluid using surface acoustic waves. Highly precise sEV fractionation without the need for sample preprocessing or complex nanofabrication methods has been demonstrated using ANSWER, showing potential as a powerful tool that will enable more in-depth studies into the complexity, heterogeneity, and functionality of sEV subpopulations.

A Flexible Meta-Curtain for Simultaneous Soundproofing and Ventilation

We demonstrate a flexible meta-curtain that can simultaneously block the propagation of sound waves of selected frequencies and let air flow through freely. Such a meta-curtain is assembled by two soft and perforated polyvinyl chloride films with an optimized distance between them. The total thickness of the meta-curtain is 1.16 cm and the holes on it have a diameter of 5 cm. The functionality of soundproofing is bestowed by the resonances formed between the films, which is verified by band structure analysis, numerical simulations, and experimental measurements. We experimentally observed sound transmission loss with a peak of 50 dB near 1700 Hz and an average of 26 dB from 1000 Hz to 1760 Hz, which is consistent with the numerical results. Attributing to the softness of the films and the robustness of the resonance, this meta-curtain retains its functionality even at deformations such as bending. Our work paves a way toward soundproof structures with the advantages of ventilation, flexibility, and light weight.

A low-frequency multiple-band sound insulator without blocking ventilation along a pipe

It is challenging to insulate sound transmission in low frequency-bands without blocking the air flow in a pipe. In this work, a small and light membrane-based cubic sound insulator is created to block acoustic waves in multiple low frequency-bands from 200 to 800 Hz in pipes. Due to distinct vibration modes of the membrane-type faces of the insulator and co-action of acoustic waves transmitting along different paths, large sound attenuation is achieved in multiple frequency-bands, and the maximum transmission loss reaches 25 dB. Furthermore, because the sound insulator with a deep subwavelength size is smaller than the cross-sectional area of the pipe, it does not block ventilation along the pipe.

Design of resonant elastodynamic metasurfaces to control S0 Lamb waves using topology optimization

Control of guided waves has applications across length scales ranging from surface acoustic wave devices to seismic barriers. Resonant elastodynamic metasurfaces present attractive means of guided wave control by generating frequency stop-bandgaps using local resonators. This work addresses the systematic design of these resonators using a density-based topology optimization formulated as an eigenfrequency matching problem that tailors antiresonance eigenfrequencies. The effectiveness of our systematic design methodology is presented in a case study, where topologically optimized resonators are shown to prevent the propagation of the S₀ wave mode in an aluminum plate.

Far-field ultrasonic imaging using hyperlenses

Hyperlenses for ultrasonic imaging in nondestructive evaluation and non-invasive diagnostics have not been widely discussed, likely due to the lack of understanding on their performance, as well as challenges with reception of the elastic wavefield past fine features. This paper discusses the development and application of a cylindrical hyperlens that can magnify subwavelength features and achieve super-resolution in the far-field. A radially symmetric structure composed of alternating metal and water layers is used to demonstrate the hyperlens. Numerical simulations are used to study the performance of cylindrical hyperlenses with regard to their geometrical parameters in imaging defects separated by a subwavelength distance, gaining insight into their construction for the ultrasonic domain. An elegant extension of the concept of cylindrical hyperlens to flat face hyperlens is also discussed, paving the way for a wider practical implementation of the technique. The paper also presents a novel waveguide-based reception technique that uses a conventional ultrasonic transducer as receiver to capture waves exiting from each fin of the hyperlens discretely. A metallic hyperlens is then custom-fabricated, and used to demonstrate for the first time, a super-resolved image with 5X magnification in the ultrasonic domain. The proposed hyperlens and the reception technique are among the first demonstrations in the ultrasonic domain, and well-suited for practical inspections. The results have important implications for higher resolution ultrasonic imaging in industrial and biomedical applications.

Constant intensity acoustic propagation in the presence of non-uniform properties and impedance discontinuities: Hermitian and non-Hermitian solutions

Propagation of sound through a non-uniform medium without scattering is possible, in principle, if the density and acoustic compressibility assume complex values, requiring passive and active mechanisms, also known as Hermitian and non-Hermitian solutions, respectively. Two types of constant intensity wave conditions are identified: in the first, the propagating acoustic pressure has constant amplitude, while in the second, the energy flux remains constant. The fundamental problem of transmission across an impedance discontinuity without reflection or energy loss is solved using a combination of monopole and dipole resonators in parallel. The solution depends on an arbitrary phase angle that can be chosen to give a unique acoustic metamaterial with both resonators undamped and passive, requiring purely Hermitian acoustic elements. For other phase angles, one of the two elements must be active and the other passive, resulting in a gain/loss non-Hermitian system. These results prove that uni-directional and reciprocal transmission through a slab separating two half spaces is possible using passive Hermitian acoustic elements without the need to resort to active gain/loss energetic mechanisms.

Acoustic transmissive cloaking with adjustable capacity to the incident direction

Zero-refractive-index (ZRI) phononic crystals (PhCs), in which acoustic waves can be transmitted without phase variations, have considerable potential for engineering wavefronts and thus are applicable to invisibility cloaking. However, the creation of the transmissive cloaking achieved by ZRI-PhCs is challenging under an oblique incidence, which substantially hinders their practical applications. Here, we experimentally demonstrate acoustic transmissive cloaking with the adjustable capacity to the incident direction. Acoustic transmissive cloaking of arbitrarily shaped obstacles can be obtained through a hybrid acoustic structure consisting of one outer layer of a programmable phase-engineered metasurface (PPEM) and one inner layer of a double zero-refractive-index (DZRI)-PhC. The DZRI-PhC is functionally the same as an equiphase area and can guide acoustic waves around the obstacle, a process known as acoustic tunneling. The PPEM perpendicularly transfers the incident acoustic waves to the DZRI-PhC and allows the emergent waves from the DZRI-PhC to transmit along the original incident direction. The DZRI-PhC is made of an array of iron squares in the air. The reciprocal of the effective bulk modulus and the effective mass density is approximately zero at a frequency of 3015 Hz (0.5187 v ₀ /a) originating from the zeroth-order Fabry-Pérot (FP) resonance that possesses infinite phase velocities. Each meta-atom of the outer metasurface consists of a line channel and four shunted Helmholtz resonators, which have effective masses that are engineered by a mechanics system. The amplitude and phase of the sound waves propagating through each meta-atom can be controlled continuously and dynamically, enabling the metasurface to obtain versatile wavefront manipulation functions. Acoustic cloaking is visually demonstrated by experimentally scanning the acoustic field over the hybrid structure at a frequency of 3000 Hz (0.5160 v ₀ /a). Our work may provide applications with great potential, including underwater ultrasound, airborne sound, acoustic communication, imaging, etc.

Metamaterial shields for inner protection and outer tuning through a relaxed micromorphic approach

In this paper, a coherent boundary value problem to model metamaterials' behaviour based on the relaxed micromorphic model is established. This boundary value problem includes well-posed boundary conditions, thus disclosing the possibility of exploring the scattering patterns of finite-size metamaterial specimens. Thanks to the simplified model's structure (few frequency- and angle-independent parameters), we are able to unveil the scattering metamaterial's response for a wide range of frequencies and angles of propagation of the incident wave. These results are an important stepping stone towards the conception of more complex large-scale meta-structures that can control elastic waves and recover energy. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

Educational open source kit for the evaluation of acoustic leaky wave antennas with metamaterials

There is a growing interest in the field of acoustic metamaterials. These materials use periodic structures to exhibit properties not usually found in nature, such as negative mass or negative compressibility. The physics supporting these devices might seem counterintuitive at first, necessitating additional educational resources in this area. A leaky wave antenna (LWA) is a good example of a practical device that can be implemented as a standard material and a metamaterial. As the latter, the device extends its operational range, linking concepts related to both versions. This work presents an experimental open source kit designed for teaching the basic notions, including a computational routine for testing its analytical performance. The kit shown in this work has interchangeable units to experiment with several configurations (slit, axisymmetric, periodic hole, and membrane based metamaterial) and parameters of the antenna's design. The kit provides an opportunity to get hands-on experience on the real-life performance of LWAs, thanks to the use of low-cost materials, minimal equipment, and the practical nature of the antenna.

Broadband impedance modulation via non-local acoustic metamaterials

Causality of linear time-invariant systems inherently defines the wave-matter interaction process in wave physics. This principle imposes strict constraints on the interfacial response of materials on various physical platforms. A typical consequence is that a delicate balance has to be struck between the conflicting bandwidth and geometric thickness when constructing a medium with desired impedance, which makes it challenging to realize broadband impedance modulation with compact structures. In pursuit of improvement, the over-damped recipe and the reduced excessive response recipe are creatively presented in this work. As a proof-of-concept demonstration, we construct a metamaterial with intensive mode density that supports strong non-locality over a frequency band from 320 Hz to 6400 Hz. Under the guidelines of the over-damped recipe and the reduced excessive response recipe, the metamaterial realizes impedance matching to air and exhibits broadband near-perfect absorption without evident impedance oscillation and absorption dips in the working frequency band. We further present a dual-functional design capable of frequency-selective absorption and reflection by concentrating the resonance modes in three frequency bands. Our research reveals the significance of over-damped recipe and the strong non-local effect in broadband impedance modulation, which may open up avenues for constructing efficient artificial impedance boundaries for energy absorption and other wave manipulation.

Broadband Sound Insulation and Dual Equivalent Negative Properties of Acoustic Metamaterial with Distributed Piezoelectric Resonators

Aiming at the unsatisfactory sound transmission loss (STL) of thin-plate structures in the low-mid frequency range, this paper proposes an acoustic insulation metamaterial with distributed piezoelectric resonators. A complete acoustic prediction model is established based on the effective medium method and classical plate theory, and the correctness is verified by the STL simulation results of the corresponding acoustic-structure fully coupled finite-element model. Moreover, the intrinsic relationship between the dual equivalent negative properties and STLs is investigated to reveal the insulation mechanisms of this metamaterial. Then, the influence of the geometric and material parameters on the double equivalent negative characteristics is studied to explore the broadband STL for distributed multi-modal resonant energy-dissipation modes in the frequency band of interest. The results show that the two acoustic insulation crests correspond to the dual equivalent negative performances, and the sound insulation in the low-mid frequency range is improved by more than 5 dB compared with that of the substrate, even up to 44.49 dB.

Microacoustic Metagratings at Ultra-High Frequencies Fabricated by Two-Photon Lithography

The recently proposed bianisotropic acoustic metagratings offer promising opportunities for passive acoustic wavefront manipulation, which is of particular interest in flat acoustic lenses and ultrasound imaging at ultra-high frequency ultrasound. Despite this fact, acoustic metagratings have never been scaled to MHz frequencies that are common in ultrasound imaging. One of the greatest challenges is the production of complex microscopic structures. Owing to two-photon polymerization, a novel fabrication technique from the view of acoustic metamaterials, it is now possible to precisely manufacture sub-wavelength structures in this frequency range. However, shrinking in size poses another challenge; the increasing thermoviscous effects lead to a drop in efficiency and a frequency downshift of the transmission peak and must therefore be taken into account in the design. In this work three microacoustic metagrating designs refracting a normally incident wave toward -35° at 2 MHz are proposed. In order to develop meta-atoms insensitive to thermoviscous effects shape optimization techniques incorporating the linearized Navier-Stokes equations discretized with finite element method are used. The authors report for the first time microscopic acoustic metamaterials manufactured using two-photon polymerization and, subsequently, experimentally verify their effectiveness using an optical microphone as a detector in a range from 1.8 to 2.2 MHz.

Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators

The wave propagation and vibration transmission in metamaterial-based elastic rods with periodically attached multi-degree-of-freedom (MDOF) dynamic anti-resonant vibration isolator (DAVI) resonators are investigated. A methodology based on a combination of the transfer matrix (TM) method and the Bloch theorem is developed, yielding an explicit formulation for the complex band structure calculation. The bandgap behavior of the periodic structure arrayed with single-degree-of-freedom (SDOF) DAVI resonators and two-degree-of-freedom (2DOF) DAVI resonators are investigated, respectively. A comparative study indicates that the structure consisting of SDOF DAVI resonators periodically jointed on the metamaterial-based elastic rod can obtain an initial locally resonant band gap 500 Hz smaller than the one given in the published literature. The periodic structure containing 2DOF DAVI resonators has an advantage over the periodic structure with SDOF DAVI resonators in achieving two resonance band gaps. By analyzing the equivalent dynamic mass of a DAVI resonator, the underlying mechanism of achieving a lower initial locally resonant band gap by this periodic structure is revealed. The parameters of the 2DOF DAVI resonator are optimized to obtain the lowest band gap of the periodic structure. The numerical results show that, with the optimal 2DOF DAVI parameters, the periodic structure can generate a much lower initial locally resonant band gap compared with the case before the optimization.

Study on Band Gap and Sound Insulation Characteristics of an Adjustable Helmholtz Resonator

To solve the problem of low-frequency noise in the environment, a Helmholtz-type phononic crystal with adjustable cavity structure and labyrinth tubes was designed. The unique design of the labyrinth tube greatly increases the length of the tube, improving low-frequency sound insulation performance, and the design of adjustable cavity structure realizes active regulation of the band structure. The band gap structure and sound insulation characteristics were analyzed by finite element method (FEM) and electro-mechanical-acoustic analogy method. The result shows that, firstly, the structure can generate two complete band gaps in the low-frequency range of 0–500 Hz, and there is a low-frequency band gap with lower limit of 40 Hz. Meanwhile, the structure has excellent sound insulation performance in the range of 0–500 Hz. Secondly, multiple resonant band gaps can be connected by adjusting the structural layout of the cavity through the telescopic screw, so as to achieve the purpose of widening the band gap and active control of environmental noise. Finally, in the periodic arrangement design of the structure, reducing the spacing between cells can effectively increase the bandwidth of band gaps. This design broadens the design idea of phononic crystal and provides a new method to solve the problem of low-frequency noise control.

Low-Frequency Low-Reflection Bidirectional Sound Insulation Tunnel with Ultrathin Lossy Metasurfaces

We report both numerical and experimental constructions of a tunnel structure with low-frequency low-reflection bidirectional sound insulation (BSI). The designed tunnel was constructed from a pair of lossy acoustic metasurfaces (AMs), which consists of six ultrathin coiled unit cells, attached on both sides. Based on the generalized Snell′s law and phase modulations for both AMs, the tunnel with the low-frequency BSI was constructed based on sound reflections and acoustic blind areas created by the AMs. The obtained transmittances were almost the same for sound incidences from both sides and were lower than −10 dB in the range 337–356 Hz. The simulated and measured results agreed well with each other. Additionally, we show that the low-reflection characteristic of the tunnel can be obtained simultaneously by thermoviscous energy loss in coiled channels of the unit cells. Finally, an interesting application of the designed tunnel in an open-window structure with low-frequency low-reflection BSI is further simulated in detail. The proposed tunnel based on the ultrathin lossy AMs has the advantages of ultrathin thickness (about λ/35), low-frequency low-reflection BSI, and high-performance ventilation, which may have potential applications in architectural acoustics and noise control.

Ultrasound-Responsive Systems as Components for Smart Materials

Smart materials can respond to stimuli and adapt their responses based on external cues from their environments. Such behavior requires a way to transport energy efficiently and then convert it for use in applications such as actuation, sensing, or signaling. Ultrasound can carry energy safely and with low losses through complex and opaque media. It can be localized to small regions of space and couple to systems over a wide range of time scales. However, the same characteristics that allow ultrasound to propagate efficiently through materials make it difficult to convert acoustic energy into other useful forms. Recent work across diverse fields has begun to address this challenge, demonstrating ultrasonic effects that provide control over physical and chemical systems with surprisingly high specificity. Here, we review recent progress in ultrasound-matter interactions, focusing on effects that can be incorporated as components in smart materials. These techniques build on fundamental phenomena such as cavitation, microstreaming, scattering, and acoustic radiation forces to enable capabilities such as actuation, sensing, payload delivery, and the initiation of chemical or biological processes. The diversity of emerging techniques holds great promise for a wide range of smart capabilities supported by ultrasound and poses interesting questions for further investigations.

Extremely low frequency wave localization via elastic foundation induced metamaterial with a spiral cavity

We proposed a metamaterial which exhibits elastic wave localization at extremely low frequencies. First, we opened an extremely low bandgap via elastic foundations. Subsequently, we investigated wave localization by imposing normal defect, which is widely used to capture waves in conventional wave localization systems. However, there were limitations: wave localization was not achieved when a weak bandgap is generated, and the operating frequency of localization is still in the upper part of the bandgap. To overcome wave localization via the normal defect, we proposed a novel metamaterial with a spiral cavity which can tune the resonating frequency depending on the length of the spiral path. By imposing on the spiral cavity inside the elastic foundation-induced metamaterial, we can shift the resonating frequency of the cavity down. Finally, we carried out wave simulations, not only to support the previous eigenfrequency study for the supercell, but also to verify that the finite-size metamaterial can also achieve wave localization at the extremely low frequencies. Through wave simulations, we could observe wave localization even at 77.3 Hz, which is definitely the lower part of the extremely low bandgap.

Leakage Effect on the Transmission Properties of a Duct Loaded with a Helmholtz Resonator

The characteristics of transmitted acoustic field have important significance to the leakage detection and the acoustic metasurface technology. When the additional leak holes are present, the conventional single neck Helmholtz resonator will naturally become the one with multiple necks. Based on such a background, in this paper, the effects of leakages on the transmission properties of a Duct Helmholtz Resonator (DHR) device is investigated both analytically and numerically. A set of closed-form formulas are derived to analytically predict the transmission spectra of the DHR device with leakages. The theoretical results are compared with COMSOL predictions. The simulation results show that the number and width of leak holes have significant influences on the amplitude, phase shift of the transmitted wave, and resonance frequency of the DHR system.

Acoustic Equivalent Lasing and Coherent Perfect Absorption Based on a Conjugate Metamaterial Sphere

Acoustic conjugate metamaterials (ACMs), in which the imaginary parts of the effective complex mass density and bulk compressibility are cancelled out in the refractive index, possess the elements of loss and gain simultaneously. Previous works have focused on panel ACMs for plane wave incidence. In this paper, we explore the extraordinary scattering properties, including the acoustic equivalent lasing (AEL) and coherent perfect absorption (CPA) modes, of a three-dimensional ACM sphere, where incident spherical waves with specific topological orders could be extremely scattered and totally absorbed, respectively. Theoretical analysis and numerical simulations show that the AEL or CPA mode with a single order can be realized with a small monolayer ACM sphere with appropriate parameters. A huge (relative to incident wavelength) ACM sphere with pure imaginary parameters could support the even- (or odd-) order AEL and odd- (or even-) order CPA modes simultaneously. In addition, the AEL and/or CPA with multiple orders could be realized based on a small multilayered ACM sphere. The proposed ACM sphere may provide an alternative method to design acoustic functional devices, such as amplifiers and absorbers.

Flexible Manipulation of the Reflected Wavefront Using Acoustic Metasurface with Split Hollow Cuboid

This work proposes a method for actively constructing acoustic metasurface (AMS) based on the split hollow cuboid (SHC) structure of local resonance, with the designed AMS flexibly manipulating the direction of reflected acoustic waves at a given frequency range. The AMS was obtained by precisely adjusting any one or two types of structural parameters of the SHC unit, which included the diameter of the split hole, the length, width, height, and shell thickness of the SHC. The simulation results showed that the AMS can flexibly manipulate the direction of the reflected acoustic waves, and the anomalous reflection angle obeys the generalized Snell’s law. Furthermore, among the five structural parameters, the AMS’s response frequency band is widest with the hole diameter and height, followed by the length and width, and narrowest with the shell thickness. It is worth noting that comprehensive manipulation of two parameters not only broadens the response frequency band, but also strengthens the effect of the anomalous reflection at the same response frequency. The subwavelength size of the AMS constructed with such a comprehensive method has the advantages of a small size, wide response band, simple preparation, and flexible modulation, and can be widely used in various fields, such as medical imaging and underwater stealth.

A transfer matrix method for calculating the transmission and reflection coefficient of labyrinthine metamaterials

Labyrinthine unit cells have existed for many years and have been central to the design of numerous metamaterial solutions. However, the literature does not present a reproducible analytical model to predict their behaviour both in transmission and reflection, thus limiting design optimization in terms of bandwidth of operation and space occupied. In this work, we present an analytical model based on the transfer matrix method for phase shift and intensity of transmission/reflection-based labyrinthine unit cells. We benchmark our analytical model by finding agreement with finite element method simulations - using commercial software - within 1 dB in amplitude and a 1° in phase. Finally, we compare our predictions with measurements on transmissive/reflective units with 4 and 6 horizontal baffles ("bars"), using different experimental methods. We found that some of the measurement methods lead to an agreement within 2 dB, while others are completely out of range, thus pointing out the challenges in characterizing this type of acoustic metamaterial.

Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.

Gaussian-Based Machine Learning Algorithm for the Design and Characterization of a Porous Meta-Material for Acoustic Applications

The scope of this work is to consolidate research dealing with the vibroacoustics of periodic media. This investigation aims at developing and validating tools for the design and characterization of global vibroacoustic treatments based on foam cores with embedded periodic patterns, which allow passive control of acoustic paths in layered concepts. Firstly, a numerical test campaign is carried out by considering some perfectly rigid inclusions in a 3D-modeled porous structure; this causes the excitation of additional acoustic modes due to the periodic nature of the meta-core itself. Then, through the use of the Delany–Bazley–Miki equivalent fluid model, some design guidelines are provided in order to predict several possible sets of characteristic parameters (that is unit cell dimension and foam airflow resistivity) that, constrained by the imposition of the total thickness of the acoustic package, may satisfy the target functions (namely, the frequency at which the first Transmission Loss (TL) peak appears, together with its amplitude). Furthermore, when the Johnson–Champoux–Allard model is considered, a characterization task is performed, since the meta-material description is used in order to determine its response in terms of resonance frequency and the TL increase at such a frequency. Results are obtained through the implementation of machine learning algorithms, which may constitute a good basis in order to perform preliminary design considerations that could be interesting for further generalizations.