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[Display omitted] • An effective framework is proposed for multi-objective optimization of elastic metamaterials. • The robust post-processing is introduced to improve the manufacturability of optimized topologies. • An in-depth study of the effects of key design parameters on multi-objective optimization is conducted. • The evolutionary mechanisms of multi-objective optimizationare explored in detail. • The physical properties and wave propagation are investigated numerically and experimentally. With respect to the wide variety of emerging applications, load-bearing capacity and harmful vibration attenuation of substructures are the principal concerns, although simultaneously satisfying both requirements is challenging. The multi-objective topological optimization framework for single-phase porous elastic metamaterials (EMs) with high efficiency and accuracy is established. Through the combination of gradient-free optimization algorithms and finite element methods, the non-dominated feasible solutions can be obtained by tailoring the periodic microstructure topology to achieve desired bandgaps (BGs) and in-plane mechanical properties. An important novelty of the proposed approach is the comprehensive investigation of the initial designs, mesh resolutions, and the symmetries of the unit cells, as well as the post-processing techniques. The results indicate that Pareto-front solutions derived from various initial designs both feature centrally distributed mass blocks that are connected with finer ligaments. In addition, the two-stage topology optimization method is introduced to effectively expand the feasible solution space at the cost of computational efficiency, and the mixed populations are utilized to accelerate convergence by 16% at least. Note that utilizing a 2D simplified model under the small deformation assumption (within the linear elasticity phase) for the optimization process requires about 3%-5% or even less time compared to utilizing a 3D model with the same optimization settings. The numerical results and experimental validation of wave propagation behavior are then carried out for wave modulation and utilization. The proposed method can be applied to structure optimization or inverse design, providing novel opportunities for the design of multifunctional periodic structures. [ABSTRACT FROM AUTHOR]

In this manuscript, we investigate deployable structures (such as solar arrays) and origami-inspired foldable structures as metamaterials capable of tunable wave manipulation. Specifically, we present a metamaterial whose bandgaps can be modulated by changing the fold angle of adjacent panels. The repeating unit cell of the structure consists of a beam (representing a panel) and a torsional spring (representing the folding mechanism). Two important cases are considered. Firstly, the fold angle (angle between adjacent beams), Ψ , is zero and only flexural waves propagate. In the second case, the fold angle is greater than zero ( Ψ > 0 ). This causes longitudinal and transverse vibration to be coupled. FEM models are used to validate both these analyses. Increasing the fold angle was found to inflict notable changes to the wave transmission characteristics of the structure. In general, increasing the fold angles caused the bandwidth of bandgaps to increase. For the lowest four bandgaps we found bandwidth increases of 252 % , 177 % , 230 % and 163 % respectively at Ψ = 90 deg (relative to the bandwidths at Ψ = 0 ). In addition, non-trivial increases in bandwidth of the odd-numbered bandgaps occurs even at small fold angles-the bandwidth for the first and third bandgaps effectively double in size (increase by 100 % ) at Ψ = 20 deg relative to those at Ψ = 0 . This could have ramifications in the context of tunable wave manipulation and adaptive filtering. In addition, by expanding out the characteristic equation of transfer matrix for the straight structure, we prove that the upper band edge of the n th bandgap will always equal the n th simply supported natural frequency of the constituent beam. Further, we found that the ratio ( E I k t ) is a pertinent parameter affecting the bandwidth of bandgaps. For low values of the ratio, effectively, no bandgap exists. For higher values of the ratio ( E I k t ), we obtain a relatively large bandgap over which no waves propagate. This can have ramifications for the design of foldable structures. As an alternative to impedance-based structural health monitoring, these insights can aid in health monitoring of deployable structures by tracking the bandwidth of bandgaps which can provide clues about the mechanical parameters of the structure. [ABSTRACT FROM AUTHOR]

This paper reports on a theoretical model of one-dimensional (1D) periodic graded metacomposites for investigating and enlarging the bandgaps in which wave propagation is not allowed. The unit-cell of the acoustic metamaterial consists of external mass, spring and internal mass. Different from the conventional infinite mass-in-mass lattice structure, the periodic metacomposite has graded internal masses in each period. Referring to lumped-mass method and on the basis of Bloch theorem, the general formula for calculating the dispersion curve of the 1D periodic graded metacomposites is derived. Furthermore, the effects of the unit-cell's parameters including the mass and the spring constants are also investigated. Numerical results show that the number of the bandgaps is closely related to the number of the unit-cells in each period. The width and the location of the bandgaps are determined by the arrangement and the values of the mass and spring constants. [ABSTRACT FROM AUTHOR]

Elastic wave propagation in honeycomb thin layers and sandwiches is investigated theoretically and numerically by using the Bloch wave transform, so the modeling of a unique primitive cell is sufficient to understand the wave propagation phenomena through the whole periodic structure. Both in-plane (with respect to the plane of the honeycomb layer) and out-of-plane waves are analyzed by developing finite element models formulated within the framework of the Mindlin–Reissner theory of plates. The dispersion relations and the phase and group velocities as function of frequency and of direction of propagation are calculated. The anisotropic behaviors and the dispersive characteristics of the studied periodic media with respect to the wave propagation are then analyzed. According to our numerical investigation, it is believed that the existence of bandgaps is probably not possible in the frequency domain considered in the present work. However, as an important and original result, the existence of the “backward-propagating” frequency bands, within which Bloch wave modes propagate backwards with a negative group velocity, is highlighted. As another important result, the comparison is made between the first Bloch wave modes and the membrane and bending/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the honeycomb media. A good comparison is obtained for honeycomb thin layers while a more important difference is observed in the case of honeycomb sandwiches, for which the pertinence of finite element models is discussed. Finally, the important role played by the honeycomb core in the flexural dynamic behaviors of the honeycomb sandwiches is confirmed. [ABSTRACT FROM AUTHOR]

• A new metamaterial MRE isolator with tunable vibration bandgaps is proposed. • A spring-mass model is built for theoretically analyses of the metamaterial MRE isolator. • The vibration isolation effectiveness increases greatly among the vibration bandgaps. • The tunable vibration bandgaps enlarge the effective frequency range of the isolator. Semi-active isolators with laminated magnetorheological elastomer (MRE) structures draw increasing attentions for vibration control because of their resonance-frequency-shift property. Their vibration attenuation capacity can be further improved by integrating the acoustic metamaterial characteristics with tunable vibration bandgaps at designed frequencies. On this basis, a novel metamaterial MRE isolator with controllable vibration bandgaps was designed and prototyped. The mechanism of the formation of vibration bandgaps was analysed theoretically using the method of mass-spring model. Both infinite and finite periodic structures were discussed respectively. The equivalent negative stiffness of the metamaterial MRE isolator was studied. The evaluation experiments were conducted to study bandgaps of the metamaterial MRE isolator and its vibration isolation capacity. Results demonstrate that the new metamaterial MRE isolator possesses controllable bandgaps and can provide improved vibration isolation performance. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we present a second nearest neighbour sp3s∗ semi-empirical tight-binding theory to calculate the electronic band structure of heterostructures based on group III-N binary semiconductors and their ternaries. The model Hamiltonian includes the second nearest neighbour (2nn) interactions, the spin–orbit splitting and the nonlinear variations of the atomic energy levels and the bond length with ternary mole fraction. Using this sp3s∗ tight-binding approach, we investigated the electronic band structure of Al1−x Ga x N/GaN and In1−x Ga x N/GaN heterostructures as a function of composition and interface strain for the entire composition range (). There is an excellent agreement between the model predictions and experiment for the principal bandgaps at , L and X symmetry points of the Brillouin zone for AlN, GaN and InN binaries and Al1−x Ga x N and In1−x Ga x N ternaries. The model predicts that the composition effects on the valence band offsets is linear, but on the conduction band offsets is nonlinear and large when the interface strain and deformation potential is large. [Copyright &y& Elsevier]

• In this study, a novel plate-type resonator used in the metamaterial sandwich plate is proposed and the band structure and the transmission spectra of the metamaterial sandwich plate are investigated. • The formation mechanisms of the bandgaps are investigated via the analysis of the mode shapes of the plate-type resonator and face plate in a unit cell. • The effect of the geometric parameters on the bandgaps is investigated and the improvement of the plate-type resonator is also discussed. In this study, a novel plate-type resonator is proposed, and the bandgap properties of a metamaterial sandwich plate containing a two-dimensional periodic array of these plate-type resonators are numerically and experimentally investigated. The finite element method is applied to calculate the band structure and the transmission spectra. The formation mechanisms of the bandgaps are investigated via the analysis of the mode shapes of the plate-type resonator and face plate in a unit cell. The results demonstrate that both locally resonant and Bragg bandgaps exist in the proposed structure. The selective coupling between the resonant modes of the plate-type resonator and the face plate is a necessary condition for the generation of locally resonant bandgaps that the resonant modes of the plate-type resonator can produce a reaction force on the support. The effect of the geometric parameters and surface mass ratio on the bandgaps is investigated, and the effect of the introduction of the plate-type resonator on the Bragg bandgap is studied. The improvements of the plate-type resonator by changing its structure or moving its attachment point are also discussed. Moreover, a metamaterial sandwich plate specimen is fabricated and vibration experiments are conducted, and it is observed that there is good agreement between the numerical predictions and the experimental results. The proposed strategy contributes to the possibility of fabricating a simpler structure to promote the exploitation of metamaterial sandwich plates in engineering. [ABSTRACT FROM AUTHOR]

This paper is concerned with the acoustic bandgap formation in a duct with periodically flush-mounted flexible walls, subject to a stream-wise temperature variation. A numerical model, based on a piecewise treatment of the arbitrary temperature gradient, is proposed for the accurate prediction of sound propagation in a complex thermal environment. Effects of the system quasi-periodicity due to the temperature change on the bandgap formation, as well as possible mitigation measures through parameter tuning, are revealed. It is shown that, on the top of the resonance bandgap, Bragg reflection bandgap can still be created despite the system quasi-periodicity. In addition to an alteration to the bandgap central frequency due to the temperature-induced acoustic wavelength changes inside the duct, the bandwidths of the bandgaps are also adversely affected, especially when the temperature gradient is large. Numerical analyses show the possibility of tuning and customizing the bandgap formation through a proper selection of the lattice distance and the structural parameters. A combined tuning strategy would warrant a merging of the bandgaps, adjustment of their central frequencies as well as an enlargement of the bandwidth for a given temperature variation range through creating a favorable coupling between the Bragg reflections and the local resonances of the flexible walls. [ABSTRACT FROM AUTHOR]