This research addresses two significant environmental impacts of urbanization and mechanization: noise pollution and ventilation. Noise pollution is increasingly recognized as a pervasive physical and mental health concern, linked to a growing array of medical conditions. Meanwhile, ventilation problems in many homes lead to excessive dampness, contributing to respiratory health issues. Current construction technology does not provide affordable solutions to these challenges, and the industry continues to rely on homogeneous materials. Cost-effective lightweight construction methods often fail to adequately reduce noise transmission between dwellings, while mechanical ventilation systems are costly, and passive trickle vents typically provide insufficient airflow. This study explores using metastructures and metasurfaces to improve sound insulation, with a focus on scalable, practical implementation. Consisting of metamaterial systems, they incorporate elements designed to reflect, absorb, and guide acoustic waves. The paper presents applications of locally resonant metamaterials, phononic crystals, subwavelength coiled acoustic resonators, and passive noise-cancellation waveguides utilizing Fano-resonance. Our findings demonstrate the effectiveness of these systems, with both experimental and simulation results showing a strong correlation. Diffuse-field testing indicates significant sound attenuation within the targeted frequency bands. We assess the advantages of each approach and identify the most effective methods.

Mechanical metamaterials demonstrate that unprecedented static and dynamic behaviors can emerge from engineered nonhomogeneous architectures. However, most designs operate at a single length scale and optimize a single performance criterion. Evidence from nature and prior studies suggests that multiscale architectures can enhance performance and broaden applications, yet their design remains challenging. To address this, a Hierarchical Metamaterial Automated Design (H-MAD) framework has been developed. This framework employs a sequential, evolutionary optimization approach to generate a population of heterogeneous structures at each scale, optimize microstructure placement and ensure cross-scale compatibility. As a case study, H-MAD is applied to 2D pentamode-like hierarchical metamaterials designed for extreme bulk-to-shear modulus ratios (B/G). The resulting architectures exhibit pentamode-like behavior across diverse configurations, demonstrating the framework's efficacy. With just two length scales, these hierarchical designs surpass both non-hierarchical structures with the same mesoscale configuration and classical pentamodes with finite joints. The best design achieves B/G approximate to 15 x 103 under bulk modulus constraints-nearly an order of magnitude higher than the baseline pentamode ratio. Even without constraints, the optimal H-MAD design attains B/G > 10 x 103, significantly outperforming conventional pentamodes. The results demonstrate that hierarchical design, combined with stiffness tailoring across scales, can enhance mechanical performance while maintaining adequate bulk moduli. The persistence of pentamode-like performance across diverse hierarchical designs indicates resilience to fabrication imperfections and material uncertainties, ensuring robust performance in practical applications. This advancement in hierarchical metamaterial design represents a step towards expanding the limits of metamaterial mechanical performance and applicability in various engineering domains.

Ordered granular structures have garnered considerable attention across various fields due to their capacity to manipulate the transmission of mechanical energy and mitigate the adverse effects of impacts and vibrations. The ability to control wave propagation is crucial in the design of protective equipment, seismic isolation systems, aerospace vibroacoustic attenuation and shock-absorbing materials, among many other applications. Here, we delve into the myriad configurations of ordered granular systems: from one dimensional granular chains to granular chain networks, showcasing their significance for pulse mitigation. Given the unique behaviours that these granular structures can generate, they can be described as discrete or granular metamaterials. A detailed analysis of the wave behaviour in these structures is presented, encompassing the influence of heterogeneity, chain curvature, and dimensional complexity on energy dissipation. This discourse extends to encompass a comparison of analytical and numerical approaches used in the examination and application of these systems, along with an exploration of the implications of advances in manufacturing methods. Unlike other examinations, this comprehensive review underscores the multifaceted nature of our study, with a steadfast focus on their applicability to impact mitigation and wave control. We conclude with a summary on the current challenges and future outlook of engineered granular systems, emphasizing their transformative potential in safeguarding structures from dynamic forces and advancing the frontier of energy management technologies.

Until relatively recently most mechanical metamaterial classes being studied have been composed of a single solid constituent phase and design has focused almost exclusively on structural geometry. Additional design dimensions can be introduced by accepting heterogeneity and varying materiality, i.e., allowing mechanical properties to vary across the metamaterial's unit cells or even from cell to cell in the metamaterial domain, creating composite metamaterials. This higher dimensionality significantly expands the effective property envelope, but the additional complexity also presents a significant hurdle. To overcome the design challenge, an automated design framework is proposed that leverages modern evolutionary computation techniques, combined with finite element analysis for fitness evaluation, to a discretized or voxelated design domain. However, this approach introduces stochastic and statistical aspects to the design process, which requires additional processing to successfully extract useful solutions. A case study is presented in which the proposed automated design framework is used to generate 2D structures that exhibit pentamode-like behavior. Pentamode metamaterials, which are best known for extreme bulk-to-shear modulus ratios (B/G), offer unique control over effective elastic properties and make for a particularly interesting test case. The evolutionary objective was defined as maximizing B/G over a voxelated square 2D domain. It was found that the evolutionary process converges to a solution relatively rapidly, generally in less that a hundred generations. B/G ratio values of 10,000 and more were obtained, largely exceeding those commonly found in the literature for experimental pentamode metamaterials. These generated designs feature reduced stress concentrations due to the elimination of point-like connections between lattice struts, which addresses a key practical limitation of diamond lattice pentamodes. It was observed that whatever the initial variety of elastic moduli values across the voxels of the design domain, as evolution progressed this variety collapsed to a much smaller number, most often a binary composite of very stiff voxels with a limited number of much softer voxels at key locations that acted as hinges.

Granular Materials (GM) employed within the mechanism of particle dampers attenuate the vibration energy due to their interparticle and particle-wall interactions. Estimating their damping effect using the analytical equivalent single mass approach overlooked the particles' individual losses that are built into the total damping. Alternatively, the numerical techniques (e.g., Discrete Element) are time-inefficient and computationally demanding. Therefore, this study explores the implementation of Machine learning (ML) algorithms to estimate the damping effect of GM. The ML model in this study will rely on a Data-Driven Modeling approach (DDM) incorporating the ensemble tress nonlinear regressor method. The models' training and testing data were obtained from an experimental setup of an acrylic beam internally integrated with Stainless Steel (SS) and glass spheres undergoing low excitation amplitude (RMS <1N). The main aim was to map between seven input features (e.g. filling ratio) and one targeted output: the beam's damped frequency response. Three ensemble trees' algorithms were used to create the DDM; Decision Tree, Random Forest, and XGBoost. The hyperparameter combination based on the Gridsearch CV function increases the prediction accuracy of each model. The developed ML models provided high accuracy (86-93%) in predicting the damping effect of the granular materials spheres.

Modern structures incorporating lightweight, low-stiffness floors face challenges for low-frequency impact noise transmission. Using spring isolators or resilient layers (e.g., floating floors) to improve isolation in light weight floor can introduce variability over time and increase structural complexity, making the system more sensitive to construction errors. An alternative approach is reviewed in this work, using internal floor cavities that contain Granular Materials (GM). Previous studies describe GM particle dampers in different applications where large movements between particles result in significant energy losses. However, a review of the experimental methods used in those studies is needed to be able to quantify the energy losses in relation to the type and degree of impact excitation. Modelling approaches are reviewed comparing their computational demand and which properties of GM are included, motion regimes and container properties. These studies span both destructive and non-destructive testing methods and give some pointers to both the geometrical and mechanical properties of granules which influence dissipation. This review goes beyond structural damping to include airborne sound absorption provided by a granular bed. This additional attenuation can be significant over a wide frequency range. A small number of practical studies of GM integrated with light weight floors show improvement in impact sound insulation. However, the lack of more detailed knowledge of GM damping mechanisms and a better understanding of GM bed interactions with containers prevents optimization of their use for insulating floors against sound transmission. This review proposes a general framework for future GM research to guide the selection of appropriate GM and addresses what is needed for optimizing lightweight floor impact sound insulation.

Most non-stochastic architected materials proposed to date have been based on periodic structures with a homogeneous topology and uniform materiality. Topologically and materially heterogeneous mechanical metamaterials promise novel capabilities, expanding the design space through growth in degrees of freedom. However, this leads to increased design complexity, as the space of possible solutions becomes a high-dimensional domain. We present a computational design automation framework for novel heterogeneous mechanical meta-material designs with a CMA-ES black-box evolutionary algorithm at its core, and demonstrate its application through a case study on new 2D pentamode meta-materials. Pentamodes are defined by extreme values of the bulk-to-shear modulus ratio (B/G) and are of particular interest due to both their unusual properties, being very stiff under compression yet easy to deform in shear, and potential as building blocks for the realization of any physically possible and desired elastic property. For the pentamode case study, this approach resulted in irregular composite structures with large B/G ratios, many structures having values between 1–3 × 104, a range well above previously reported experimental values of 103. The new meta-material systems it generated do not present the point-like connections of the classic pentamode diamond-type lattice, which is a key practical limitation for application. This work shows that population-based metaheuristic computational methods can reliably generate novel mechanical metamaterial designs capable of achieving more extreme performance than more traditional metamaterial design approaches.

Recognizing the need for effective control of vibration and sound propagation in various industries, this study investigates the potential of designing heterogeneous granular networks for vibroacoustic transmission mitigation. It introduces new models of granular systems: decorated, stepped, and tapered 2-level branching structures. The research assesses changes in particle size (5–10 mm radii) and material properties (density and Young's Modulus) to create finely-tuned composites that significantly modulate pulse waves. The discrete element method predicts wave propagation in these granular metamaterials, comparing monodispersed chains, conventional chain networks, and the proposed heterogeneous structures. Their pulse diffusion capacity is evaluated, showing how collective responses can be adjusted by altering physical parameters like particle size and composition. Preliminary findings underscore the utility of these configurations in advancing the development of elastic and acoustic metamaterials, demonstrating a peak amplitude reduction more than five times greater than an equivalent monomer system. With versatility across a wide frequency range, these metamaterials could pioneer a new direction in impact mitigation.

Research in mechanical metamaterials has achieved extreme, unprecedented properties by exploiting inhomogeneity in the form of periodic structures, enabled by advances in digital computation and manufacturing. The result has been a proliferation of metamaterials and relatively recently, the emergence of non-periodic heterogeneous metamaterial systems, which we term metastructures. This represents the beginnings of the evolution of metamaterials from just materials with unique properties towards systems capable of more complex, machine-like functions. To better understand the essential features and relationships among this wide and growing variety of species within the classes of mechanical metamaterials and metastructures, a classification scheme that focuses on functionality is needed. Both periodic and non-periodic metamaterials systems can be abstracted as mechanisms that produce desired outputs by performing specified transformations on given mechanical inputs. Here we propose an approach to functional classification and comparison based on the deformation and force transformations that these metamaterials and metastructures can provide. Transformation- based approaches are prevalent in geometry processing, computer graphics and soft robotics. This review examines existing periodic and non-periodic metamaterials from this perspective, classifying them according to the quasi-static deformation output they can achieve, and identifying gaps, challenges and promising future directions. Two classes of transformations are defined, i.e., uniformly distributed (homogeneous) or spatially dependent (non-homogeneous), and their building blocks and mechanisms are discussed. This stance empowers a more efficient approach to inverse design of metamaterial systems, in which desired operations are realized through transformations produced by the combination of diverse building-block architectures.

Metamaterials and architected materials derive their effective properties from their internal structure more than from their composition. While the variety of metamaterial structures is limitless in principle, in practice, metamaterials have tended to be based on periodic structures with a homogeneous topology, which limits the range of properties that can be achieved. The metamaterial design space can be expanded by accepting irregularity, a step towards discarding the bonds of periodicity and topological uniformity. Varying materiality, that is allowing the mechanical properties of the metamaterial’s constituent material to vary, introduces additional design dimensions. Here, an evolutionary framework is proposed to search for solutions in these expanded design spaces. It relies on a modern evolutionary computation technique combined with conventional deterministic modelling, in the form of finite element analysis, executed on a massively parallel computing system. This approach produces large amounts of data, introducing stochastic and statistical aspects to the design process, and the extraction of useful solutions is discussed. A case study is presented in which the bulk-to-shear modulus ratio (B/G) of a voxelised square 2D domain is maximised by our evolutionary framework. Extreme values the B/G ratio are the defining characteristic of pentamode metamaterials, which make for a particularly interesting test case because they offer a path towards unparalleled control over effective mechanical properties. B/G ratio values of 10,000 and more were obtained, largely exceeding those commonly found in the literature for pentamode metamaterials that have been tested. In addition, the designs generated by this evolutionary approach eliminate the need for point-like connections between lattice struts, which addresses a key practical limitation of existing pentamodes.

Reduction in sound transmission through walls and ceilings, particularly at lower frequencies, is important both because of ongoing growth in noise pollution and the challenges faced in providing good sound insulation with existing construction methods. Mechanical metamaterials can help address these challenges by enabling the creation of an artificial medium that produces significantly greater attenuation than existing passive lightweight material constructions. In part one of this work we designed, modelled and tested simple local resonance structures (LRS) to investigate their potential for future acoustic insulation systems. In part two we extend this work to multilayer and multi-resonance systems. Three LRS families have been studied: multilayer with single resonance, multilayer with multiple resonances and intermediate layer with single resonance. Comparisons are presented based on lumped parameter modelling and transmission loss (TL) measurements under plane wave acoustic excitation. The LRS designs achieved peak transmission losses up to 40 dB greater than non-resonant structures of equivalent surface density within a specified frequency range, and exhibited gains having bandwidths up to 300 Hz. The depth and width of the attenuation bands were found to be controlled by different design parameters, so systems with appropriately tuned interlayer couplings and resonator stiffness exhibited large increases in magnitude and bandwidth of the attenuation. Furthermore, the distribution of stiffness, damping and mass in the resonators powerfully affected the shape of the TL spectrum, and could be used to keep TL at or above mass law levels throughout. LRS systems have the potential to provide significantly higher transmission loss at low frequencies than conventional wall systems of similar size and weight. This is a step towards a locally resonant architecture that can be incorporated into a practical insulation system. (C) 2021 Elsevier Ltd. All rights reserved.

Worldwide increases in noise levels due to growth in urban population, traffic and machinery have serious implications for health, productivity and quality of life. Prevention of sound transmission through walls and ceilings, particularly towards the lower frequency range of human hearing is important both because of its recent increase in levels and the challenges faced when providing sound insulation of long wavelength noise with existing construction methods. Mechanical metamaterials have the potential to address these challenges by enabling the creation of an artificial medium that generates far more attenuation of wave transmission than any existing material system. In part one of this work we design, model and test several local resonance structure (LRS) systems to provide the basis for future acoustic insulation systems. Three different LRS families were studied: spherically symmetric, flexural single-resonance and flexural multi-resonance. Some resonator elements showed a peak effective mass up to fifty times greater than their rest mass and achieved peak transmission losses 10s of dB greater than a non-resonant structure of equivalent surface density within the designated frequency range. By arranging sets of resonators with closely spaced resonance frequencies the transmission loss gains were spread over a wider frequency range and a reduction in the transmittance peak at the upper end of the band gap was achieved though variations in damping and mass of the resonators. A large (2.5 m(2)) test article was constructed and tested under full scale diffuse field conditions such as are found in buildings. The results confirmed that the band gap observed in impedance tube measurements of small-scale LRS specimens survives. Modelling and testing results for more multilayer and multi-resonance systems are presented in part 2. (C) 2020 Elsevier Ltd. All rights reserved.

Limitations of the traditional manufacturing methods often force engineered components to be made of single material systems. However, this is going through changes due to the advent of additive manufacturing (AM) methods, as the point-by-point consolidation allows for a possible change of the material constitution within a given part domain. This will give rise to a plethora of new material and property options for the designers, where just human perception may fail to realize the full benefits. Automated design tools integrating material choice, dispersion, analysis, and optimization algorithms need to be developed to assist in finding the optimal multi-material dispersion solutions achieving given performance criteria sets. Considering the fact that the multi-material manufacturing systems are only recently coming into use, design solutions targeting optimal placement of multiple materials are not common. This article addresses this gap, evaluating a numerical model integrated with different optimization schemes to find the optimal material solutions achieving certain preset performance criteria such as combinations of natural frequencies in different degrees of freedom. A case study of three different metaheuristic optimization schemes based on genetic algorithms indicates, first, that it is possible to create a beam with six uniformly spaced natural frequencies and to change these frequencies without modifying the structural geometry; and second that the basic genetic algorithm generally outperforms neural net-based alternatives for this problem. This tailoring of the structural resonance spectrum demonstrates that evolutionary computing combined with multi-material AM can be used to unlock previously unavailable structural functionality.

This paper reports an alternating current (AC) thermal flow sensor, based on the 3ω method, capable of measuring fluid flow in stacked microfluidic channels and through separating membranes. The measurement concept is tested in a triple-layer polydimethylsiloxane (PDMS) device containing two parallel channels separated by a membrane. A 3ω element integrated into the bottom channel was used to determine the flow direction and magnitude in both channels. Our results show that the phase of the temperature wave is linked not only to fluid velocity, but the physical dimensions of the channel, thus providing a novel non-contact tool to probe fluid flows.

This paper presents a novel experimental and simulation investigation of quasi-static transverse deformation of 3D printed polymeric Functionally Graded (FG) plates, which obey the distribution of material properties through the length. Graded solid elements with continuous property distribution at different Gauss points were implemented by a user material subroutine (UMAT) in ABAQUS Finite Element (FE) software. In order to validate the proposed graded FE solutions, the original experimental deflection measurements using 3D-Digital Image Correlation (DIC) technique performed to capture transverse deformation of designed and manufactured 3D printed polymeric FG plates. DIC technique involved tracking the motion of geometric features on a specimen surface over the course of an experiment to generate the displacement field experimentally. It was found that the deviation between FE and experimental out of plane deflection for nonlinear FG plates is higher than that of linear FG plates, which is potentially due to the high gradient distribution of the material inclusions. It can be concluded that the presented 3D-digtal image correlation technique provides for transverse deformation of polymeric FG plates. The deflection contours for the FG plate are not symmetric, differences being more prominent for the linear high stiffness ratio combination. The outcomes of this study can be applied to determine the optimum material distribution to produce a controlled-stiffness polymeric FG plate corresponding to prescribed structural characteristics.

Auxetic structures exhibit negative Poisson’s ratios based on the deflection characteristics of the macrostructural forms generated by integrating specific base units. Considering the advantages of the abnormal metamaterial behavior, auxetic structures attained considerable research attention. While theoretical predictions indicate the possibilities to achieve very high auxetic responses, practical implementation and experimental validation were limited due to the difficulties in manufacturing the complex structural forms. Practical realization of true auxetic structural solutions attained a great impetus with the advent of the additive manufacturing solutions, opening up wider opportunities and renewed interests. The current research is an attempt towards enhancing the auxetic nature of a square grid structure by numerical and experimental methods. Finite element simulations allowed to identify structural changes for improved auxeticity and experimental validation based on selective laser melted structures proved the trends to be true. Experimental results based on the fabricated structure indicate the Poisson’s ratio to be − 7.

Wave propagation through a structured medium has attracted the attention of researchers for centuries due to its relevance to problems in condensed matter physics, chemistry, optics, phononics, composite, acoustics and mechanics. Wave containing certain band of frequencies can either propagate, known as transmission, or attenuated, known as attenuation band. This band structure for a continuum and its equivalent lumped spring mass model are not identical, although continuum medium is often modelled as a chain of discrete periodic structures because the continuous and discrete is depends on the scale. These band characteristics are dependent on the properties of the units, thus the effects of different parameters, such as damping, stiffness and mass ratios, nonlinearity, on the bandwidth are compared with each other in this review. To cloak, modulate, guide, filter out or attenuate unwanted frequencies from the propagating waves, metamaterials are widely investigated as a special form of the periodic structures from the past 2 decades. The main aim of this review is to compare the bandwidth for one-dimensional periodic structures. Waves through two and three-dimensional periodic medium are not considered in the review because the key band characteristics of periodic system can be perceived in one dimensional. The methods for computing the wave transmission are evaluated in the non-dimensional domain and the band characteristics of different one-dimensional periodic structures are critically assessed in this review. This review will help to the future researchers to choose a proper periodic medium for getting a specific band phenomenon.

Due to the out of phase vibration of the internal units, unusual frequency dependent extreme properties, such as negative effective mass, can be perceived in a metamaterial. However, the performance of the linear metamaterial is limited to a narrow bandwidth due to the dependency on linear resonance. In this paper, this main limitation of the metamaterial is addressed by introducing the piecewise linear impacting oscillator at the mass in-mass resonating unit. The impacting system dissipates energy and consequently attenuates the vibration of the main structure due to the counteraction of the external excitation by the resulting impulse force. Attenuation bandwidths can be increased in higher and lower frequency side for impact metamaterial as it can attenuate the two transmission peaks. In the lower frequency side attenuation bandwidth can be increased 50% and in the higher frequency side it theoretically becomes infinite. Therefore, impacting metamaterial can be considered as a potential solution towards low frequency and wideband vibration isolator. This paper also thoroughly discussed different nonlinear responses in each units of metamaterial chain.

Vibration transmission through a mass-in-mass unit is frequency dependent due to the difference in phase between the internal resonator and the surrounding structure. Generally, the attenuation band is confined between the two-transmission bands for a linear resonating metamaterial. In the case of a linear metamaterial, the attenuation band can be widened up to a certain limit by tuning the material properties, but cannot be extended infinitely by removing the 2nd transmission band. An impacting resonator can attenuate the vibration of the metamaterial due to the counteraction of the external excitation by the resulting impulse force and due to the presence of the sub and super-harmonic and chaotic responses. This paper theoretically elucidates that an impact metamaterial can results zero averaged effective mass for the multi-periodic type impacting vibration as in these frequency ranges vibration becomes essentially out of phase. Most importantly, an impacting metamaterial has a potential to extend the attenuation bandwidth by reducing the vibration of the main structure even for the minimal mass ratio. The scope of the paper is limited to analysis of a single building block of the impacting metamaterial to provide better insight comprehension of the effect of impacting oscillation inside a metamaterial unit more systematically.