This work aims to compare the capability of vibration attenuation by standard elastomeric polymers, and by the new anomalously damping nematic liquid crystal elastomer. We use the most mainstream materials in both categories, and design two testing platforms: the ASTM-standard constrained layer plate resonance geometry, and the attenuation of resonances in a commercial device (electric drill) where the damping polymers were inserted into the casing. In the standard plate resonance testing, we find that LCE outperforms all standard damping materials, moreover, it brings the vibrating plate into the overdamped condition, which is unique for a non-fluid dissipative system. In the attenuation of high-frequency vibrations of a device, we also found LCE dissipates these vibrations much better, although we did not find the optimal insertion configuration for the damping polymer, and did not reach overdamping.

This paper presents a novel Flexnertia metastructure concept to perform vibration suppression through coupling rotational inertia to structural flexural motion. Theoretical analysis and experimental test of the proposed metastructure with emphasis on dissipating structural flexural motion is exhibited, showing vibration control performance. The experimental and numerical results are in good agreement, both confirming that the average overall response of the metastructure is significantly reduced. The attenuation becomes most pronounced in the low-frequency range where structures tend to suffer most due to high response around the regime of the first flexural modes.

Acoustic metastructures exhibit an unprecedented ability to arbitrarily manipulate the properties of sound waves, including amplitude and phase modulation which has attracted much attention in both the academic and industrial communities. Design of metastructures has been extensively investigated for the purpose of the independent manipulation of acoustic and elastic waves. It is up to now unclear however if the optimal dissipation approach involves locally resonant structural elements, or locally resonant acoustic cavities or a hybrid mix of both noise abatement mechanisms. To study this problem, we investigate numerically and experimentally the noise reduction performance of acoustic and mechanically locally resonant structures and how they perform when integrated into the same application scenario. Taking the noise emission of an electric motor as the excitation regime for our study, the acoustic and mechanical metamaterial structures with respective C-shape and T-shaped resonators are judiciously designed to maximize noise dissipation within two targeted frequency bands where the motor noise peaks. A hybrid structure with a mix of both resonators is also designed. The results demonstrate that all three metastructure designs improved the noise attenuation performance with an additional sound insertion loss of up to 16 dB when compared to a flat wall structure of equivalent mass. The findings in this work demonstrate that significant noise attenuation can be obtained by incorporating these acoustic and mechanical meta-atoms into a wall architecture which may have great potential for real world applications such as surrounding electric motors which tend to emit monotonic and irritating noise.

There is an increasing need for supply chains that can rapidly respond to fluctuating demands and can provide customised products. This supply chain design requires the development of flexibility as a critical capability. To this end, firms are considering Additive Manufacturing (AM) as one strategic option that could enable such a capability. This paper develops a conceptual model that maps AM characteristics relevant to flexibility against key market disruption scenarios. Following the development of this model, a case study is undertaken to indicate the impact of adopting AM on supply chain flexibility from four major flexibility-related aspects: volume, mix, delivery, and new product introduction. An inter-process comparison is implemented in this case study using data collected from a manufacturing company that produces pipe fittings using Injection Moulding (IM). The supply chain employing IM in this case study shows greater volume and delivery flexibility levels (i.e., 65.68% and 92.8% for IM compared to 58.70% and 75.35% for AM, respectively) while the AM supply chain shows greater mix and new product introduction flexibility, indicated by the lower changeover time and cost of new product introduction to the system (i.e., 0.33 h and €0 for AM compared to 4.91 h and €30,000 for IM, respectively). This work will allow decision-makers to take timely decisions by providing useful information on the effect of AM adoption on supply chain flexibility in different sudden disruption scenarios such as demand uncertainty, demand variability, lead-time compression and product variety.

Nematic liquid crystal elastomers (LCE) exhibit unique mechanical properties, placing them in a category distinct from other viscoelastic systems. One of their most celebrated properties is the 'soft elasticity', leading to a wide plateau of low, nearly-constant stress upon stretching, a characteristically slow stress relaxation, enhanced surface adhesion, and other remarkable effects. The dynamic soft response of LCE to shear deformations leads to the extremely large loss behaviour with the loss factor tanδ approaching unity over a wide temperature and frequency ranges, with clear implications for damping applications. Here we investigate this effect of anomalous damping, optimising the impact and vibration geometries to reach the greatest benefits in vibration isolation and impact damping by accessing internal shear deformation modes. We compare impact energy dissipation in shaped samples and projectiles, with elastic wave transmission and resonance, finding a good correlation between the results of such diverse tests. By comparing with ordinary elastomers used for industrial damping, we demonstrate that the nematic LCE is an exceptional damping material and propose directions that should be explored for further improvements in practical damping applications.

In this work, we present a single low-profile metamaterial that provides bandgaps of acoustic and elastic waves at the same time. This was done by ensuring impedance mismatch in two different domains, the fluid domain where the acoustic waves propagate and the solid domain where the elastic waves propagate. Through creatively designing the metamaterial, waves of certain nature and frequencies of interest were completely blocked in the solid and fluid domains simultaneously. The simulation results showed bandgaps with acoustic waves attenuation below 5 kHz and elastic waves attenuation below 10 kHz. The acoustic and elastic dispersion curves of the metamaterials were calculated for various designs with various diameters and neck lengths, and the bandgaps were calculated. These parameters can be used as means for tuning both the acoustic and elastic bandgaps. A representative design of the metamaterial was manufactured on a laser powder bed fusion system and the dynamic performance was measured at various points. The measurements were carried out using a dynamic shaker setup and the dynamic performance was in good agreement with the numerical modelling results. Such metamaterials can be used for simultaneous acoustic and elastic attenuation, as well as saving in space and material consumption, in various fields including building construction, automobile, aerospace and rocket design.

This paper investigates dynamic properties of 3D rainbow lightweight hollow sphere foams both numerically and experimentally. Two rainbow hollow sphere foams are designed with linearly varying sphere shell thicknesses and binder diameters for the purpose of achieving broadband vibration attenuation at low frequencies. The hollow sphere foams are modeled by the finite element method. The band structures of two rainbow hollow sphere foams are compared with that of the uniform foam. The results show that the foam with gradient binders exhibits a bandgap more than two times broader than that of the uniform foam at lower frequencies, and the gradient binders also lead to locally concentrated vibration modes at the bandgap edges, which are different from the global vibration modes of the uniform foam. On the other hand, the foam with gradient shell thickness could not generate complete bandgaps due to the introduced additional modes by the varied shell thickness. The bandgap extension could, hence, be realized with properly designed structural gradients of foams. The rainbow and uniform hollow sphere foam samples are manufactured subsequently by the additive manufacturing method and tested with a frequency response function measurement system. The experimental results verify the numerical calculation as well as prove further the effects of gradient designs on bandgap extension. The proposed rainbow hollow sphere foams could be instructive for future researchers to design lightweight acoustic/dynamic structures for broadband low frequency noise and vibration control.

We hereby report for the first time on the design, manufacturing and testing of a three-dimensional (3D) nearly-periodic, locally resonant phononic crystal (PnC). Most of the research effort on PnCs and metamaterials has been focused on the enhanced dynamic properties arising from their periodic design. Lately, additive manufacturing techniques have made a number of designs with intrinsically complex geometries feasible to produce. These recent developments have led to innovative solutions for broadband vibration attenuation, with a multitude of potential engineering applications. The recently introduced concept of rainbow metamaterials and PnCs has shown a significant potential for further expanding the spectrum of vibration attenuation in such structures by introducing a gradient profile for the considered unit cells. Given the above, it is expected that designing non-periodic PnCs will attract significant attention from scientists and engineers in the years to come. The proposed nearly-periodic design is based on cuboid blocks connected by curved beams, with internal voids in the blocks being implemented to adjust the local masses and generate a 3D rainbow PnC. Results show that the proposed approach can produce lightweight PnCs of a simple, manufacturable design exhibiting attenuation bandwidths more than two times larger than the equivalent periodic designs of equal mass.

In this study, we propose a 'rainbow' metamaterial to achieve broadband multi-frequency vibration attenuation. The rainbow metamaterial is constituted of a Π-shaped beam partitioned into substructures by parallel plates insertions with two attached cantilever-mass acting as local resonators. Both resonators inside each substructure can be non-symmetric such that the metamaterial can have multi-frequency bandgaps. Furthermore, these cantilever-mass resonators have a progressively variant design along the beam, namely rainbow-shaped, for the purpose of achieving broader energy stop bands. Π-shaped beams partitioned by parallel plate insertions can be extended to honeycomb sandwich composites, hence the proposed rainbow metamaterial can serve as a precursor for future honeycomb composites with superior vibration attenuation for more industrial applications. A mathematical model is first developed to estimate the frequency response functions of the metamaterial. Interaction forces between resonators and the backbone structure are calculated by solving the displacement of the cantilever-mass resonators. The plate insertions are modeled as attached masses with both their translational and rotational motion considered. Subsequently, the mathematical model is verified by comparison with experimental results. Metamaterials fabricated through an additive manufacturing technique are tested with a laser doppler receptance measuring system. After the validation of the mathematical model, a numerical study is conducted to explore the influences of the resonator spatial distributions on the frequency response functions of structures. Results show that for metamaterials with both symmetric and non-symmetric resonators, rainbow-shaped resonators can introduce inertial forces inside wider frequency range when compared to the periodic resonators of the same total mass, hence broader bandgaps. Meanwhile, the attenuation inside the bandgaps decreases when the bandgap become broader. Metamaterials with broadband multi-frequency range vibration attenuation can be achieved with non-symmetric sinusoidally varying resonators.

Recent advances in additive manufacturing have enabled fabrication of phononic crystals and metamaterials which exhibit spectral gaps, or stopbands, in which the propagation of elastic waves is prohibited by Bragg scattering or local resonance effects. Due to the high level of design freedom available to additive manufacturing, the propagation properties of the elastic waves in metamaterials are tunable through design of the periodic cell. In this paper, we outline a new design approach for metamaterials incorporating internal resonators, and provide numerical and experimental evidence that the stopband exists over the irreducible Brillouin zone of the unit cell of the metamaterial (i.e. is a three-dimensional stopband). The targeted stopband covers a much lower frequency range than what can be realised through Bragg scattering alone. Metamaterials have the ability to provide (a) lower frequency stopbands than Bragg-type phononic crystals within the same design volume, and/or (b) comparable stopband frequencies with reduced unit cell dimensions. We also demonstrate that the stopband frequency range of the metamaterial can be tuned through modification of the metamaterial design. Applications for such metamaterials include aerospace and transport components, as well as precision engineering components such as vibration-suppressing platforms, supports for rotary components, machine tool mounts and metrology frames.

We report on numerical modelling of three-dimensional lattice structures designed to provide phononic bandgaps. The examined lattice structures rely on two distinct mechanisms for bandgap formation: the destructive interference of elastic waves and internal resonance. Further to the effect of lattice type on the development of phononic bandgaps, we also present the effect of volume fraction, which enables the designer to control the frequency range over which the bandgaps exist. The bandgaps were identified from dispersion curves obtained using a finite element wave propagation modelling technique that provides high computational efficiency and high wave modelling accuracy. We show that lattice structures employing internal resonance can provide transmissibility reduction of longitudinal waves of up to -103 dB. Paired with the manufacturing freedom and material choice of additive manufacturing, the examined lattice structures can be tailored for use in wide-ranging applications including machine design, isolation and support platforms, metrology frames, aerospace and automobile applications, and biomedical devices.

In this paper, the phonon dispersion curves of several surface-based lattices are examined, and their energy transmission spectra, along with the corresponding bandgaps are identified. We demonstrate that these bandgaps may be controlled, or tuned, through the choice of cell type, cell size and volume fraction. Our results include two findings of high relevance to the designers of lattice structures: (i) network and matrix phase gyroid lattice structures develop bandgaps below 15 kHz while network diamond and matrix diamond lattices do not, and (ii) the bandwidth of a bandgap in the network phase gyroid lattice can be tuned by adjusting its volume fraction and cell size.

This paper presents the design, analysis and experimental verification of strut-based lattice structures to enhance the mechanical vibration isolation properties of a machine frame, whilst also conserving its structural integrity. In addition, design parameters that correlate lattices, with fixed volume and similar material, to natural frequency and structural integrity are also presented. To achieve high efficiency of vibration isolation and to conserve the structural integrity, a trade-off needs to be made between the frame's natural frequency and its compressive strength. The total area moment of inertia and the mass (at fixed volume and with similar material) are proposed design parameters to compare and select the lattice structures; these parameters are computationally efficient and straight-forward to compute, as opposed to the use of finite element modelling to estimate both natural frequency and compressive strength. However, to validate the design parameters, finite element modelling has been used to determine the theoretical static and dynamic mechanical properties of the lattice structures. The lattices have been fabricated by laser powder bed fusion and experimentally tested to compare their static and dynamic properties to the theoretical model. Correlations between the proposed design parameters, and the natural frequency and strength of the lattices are presented.