Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences最新文献

Periodic wave barriers (PWB) open a new window for vibration mitigation. However, the Doppler effect is rarely considered in most of the previous investigations on the control of ambient vibration induced by moving loads. This article reveals the significance of the speed and frequency of moving loads on surface waves, and improves the design method of PWB for ambient vibration reduction and isolation. First, the theoretical expression of the main frequency band of surface waves propagating in an elastic half-space caused by a moving load was obtained. Comparisons with the numerical results under three different types of traffic loads were also conducted and good agreement was found. Second, the theoretical expression and numerical results were verified by experimental studies. Some inherent properties of wave propagation caused by a moving load in an elastic half-space were also revealed. Third, two kinds of PWBs, i.e. periodic empty trench barrier and periodic pile barrier, were introduced to mitigate wave propagation. It has been confirmed that if the attenuation zones of PWB match the target frequency bands given by the theoretical expression, good vibration mitigation can be achieved. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Periodic wave barriers have been widely used to manipulate elastic waves propagating in saturated and single-phase soil due to their attenuation zone properties. However, it is difficult to promote application of periodic barriers in unsaturated soils due to their complex constitutive relationship. In this study, manipulation of surface waves by periodic in-filled trench barriers in unsaturated soil has been studied based on the periodic theory. The dispersion relations of a periodic structure for surface waves in unsaturated soil are determined. The attenuation mechanism of evanescent surface waves is revealed. Next, the effects of several key parameters of unsaturated soil on the attenuation zones of the periodic in-filled trench barriers are comprehensively discussed. It is found that in a particular range for material parameter, the surface waves are attenuated over the entire frequency range due to the viscosity of fluid. Finally, a periodic in-filled trench barrier is designed according to a field test of ground vibration induced by a train, and its performances in mitigating surface waves propagating in unsaturated and saturated soils are conducted and compared by conducting analysis in time domain. This investigation provides a new insight for manipulating surface waves by periodic barriers. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

In this work, we propose elastic metamaterials with phase discontinuities to steer the propagation of near-source bulk waves in a semi-infinite elastic medium. Our design exploits an array of embedded subwavelength resonators with tailored masses to attain a complete phase shift spanning [Formula: see text]. This phase control allows for diverse wave functionalities, such as directional refraction and energy focusing. Through the use of dispersion diagrams and the generalized Snell's law, along with a multiple scattering formulation, we analytically demonstrate the effectiveness of our design in achieving the desired wavefront manipulation. The proposed design has the potential to advance the field of guiding elastic waves using metamaterials and find practical applications in areas such as isolating ground-borne vibrations in densely urbanized regions and energy harvesting. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Many deployable structures in nature, as well as human-made mechanisms, preserve symmetry as their configurations evolve. Examples in nature include blooming flowers, dilation of the iris within the human eye, viral capsid maturation and molecular and bacterial motors. Engineered examples include opening umbrellas, elongating scissor jacks, variable apertures in cameras, expanding Hoberman spheres and some kinds of morphing origami structures. In these cases, the structures either preserve a discrete symmetry group or are described as an evolution from one discrete symmetry group to another of the same type as the structure deploys. Likewise, elastic metamaterials built from lattice structures can also preserve symmetry type while passively deforming and changing lattice parameters. A mathematical formulation of such transitions/deployments is articulated here. It is shown that if [Formula: see text] is Euclidean space, [Formula: see text] is a continuous group of motions of Euclidean space and [Formula: see text] is the type of the discrete subgroup of [Formula: see text] describing the symmetries of the deploying structure, then the symmetry of the evolving structure can be described by time-dependent subgroups of [Formula: see text] of the form [Formula: see text], where [Formula: see text] is a time-dependent affine transformation. Then, instead of considering the whole structure in [Formula: see text], a 'sector' of it that lives in the orbit space [Formula: see text] can be considered at each instant in time, and instead of considering all motions in [Formula: see text], only representatives from right cosets in the space [Formula: see text] need to be considered. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Predicting failure initiation in nonlinear composite materials, often referred to as metamaterials, is a fundamental challenge in nonlinear solid mechanics. Microstructural failure mechanisms encompass fracture, decohesion, cavitation, compression-induced contact and instabilities, affecting their unconventional static and dynamic performances. To fully take advantage of these materials, especially in extreme applications, it is imperative to predict their nonlinear behaviour using reliable, accurate and computationally efficient numerical methodologies. This study presents an innovative nonlinear homogenization-based theoretical framework for characterizing the failure behaviour of periodic reinforced hyperelastic composites induced by reinforcement/matrix decohesion and interaction between contact mechanisms and microscopic instabilities. Debonding and unilateral contact between different phases are incorporated by employing an enhanced cohesive/contact model, which features a special nonlinear interface constitutive law and an accurate contact formulation within the context of finite strain continuum mechanics. The theoretical formulation is demonstrated using periodically layered composites subjected to macroscopic compressive loading conditions along the lamination direction. Numerical results illustrate the ways in which debonding phenomena, in conjunction with fibre microbuckling, may influence the critical loads of the examined composite solid. The sensitivity of the results obtained through the proposed contact-cohesive model at finite strain with respect to its implementation is also explored. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

In this work, we investigate the dynamics of Scholte-Stoneley waves (SSWs) travelling along elastic metasurfaces, e.g. thin resonant structures embedding mechanical oscillators, placed at the interface between solid and fluid. To this purpose, an analytical dispersion law, valid in the long-wavelength regime, is derived and used to reveal the hybridization of SSWs with the collective resonance of the mechanical oscillators and the conversion of SSWs into leaky modes within the fluid. The analytical predictions are validated through numerical simulations that include both dispersive and harmonic analysis. Our findings disclose the capabilities of elastic metasurfaces in filtering, trapping and converting SSWs along fluid-solid interfaces, thus supporting the design of novel devices for solid-fluid interaction across various engineering applications, including microfluidics. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

This article focuses on characterizing a class of quasi-periodic metamaterials created through the repeated arrangement of an elementary cell in a fixed direction. The elementary cell consists of two building blocks made of elastic materials and arranged according to the generalized Fibonacci sequence, giving rise to a quasi-periodic finite microstructure, also called Fibonacci generation. By exploiting the transfer matrix method, the frequency band structure of selected periodic approximants associated with the Fibonacci superlattice, i.e. the layered quasi-periodic metamaterial, is determined. The self-similarity of the frequency band structure is analysed by means of the invariants of the symplectic transfer matrix as well as the transmission coefficients of the finite clusters of Fibonacci generations. A high-frequency continualization scheme is then proposed to identify integral-type or gradient-type non-local continua. The frequency band structures obtained from the continualization scheme are compared with those derived from the Floquet-Bloch theory to validate the proposed scheme. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1).'

In this work, the Schwarz primitive unit cell is used as the building block of different types of metastructures for steering and focusing elastic vibrations. The emergence of a Bragg-type bandgap when constructing a two-dimensional plate from such unit cells is experimentally validated. It is demonstrated that increasing both mass and porosity of the Schwarz primitive leads to a decrease in the frequency of the out-of-plane propagating wave targeted in this study. By arranging these modified Schwarz primitive unit cells in constant and graded layouts, two-dimensional plates with an embedded metabarrier and a metalens are numerically designed. The metabarrier protects an interior area of the plate from the propagating waves on a wide frequency band (approx. 1.4-3.4 kHz). Equally, the refractive index profile necessary for gradient index lenses is obtained via a progressive variation of the added mass or, alternatively, the porosity of the unit cell over a rectangular area. For the first time, bending of the out-of-plane mode towards the focusing point is practically validated in a challenging mesoscale experiment requiring the assembly of different three-dimensional printed sections of the plate. The increased porosity design is advantageous not only in terms of overall lightweight, but also towards additive manufacturing as it requires less material.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

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)'.

The unique properties of metamaterials are determined by the configuration and spatial arrangement of artificially designed unit structures. However, the configuration and mechanical properties of conventional metamaterials are challenging to reverse and adjust. Based on curved beams, two types of novel three-dimensional (3D) multi-stable metamaterials with reconfigurable deformation and tunable mechanical properties are designed and fabricated using a four-dimensional (4D) printing method. The effects of temperature and curved-beam thickness on the force-displacement curves and multi-stable snapping sequence of the 3D multi-stable metamaterials are investigated by finite-element analysis (FEA) and experiments. In addition, based on the designed four-branch multi-stable metamaterials, three- and six-branched multi-stable structures are designed by changing the number of curved-beam branches. It is shown that, owing to shape memory effects, the 3D multi-stable metamaterials can realize mechanical programmability, and the multi-stable deformation sequence can be precisely regulated by varying the temperature and curved-beam thickness. These 4D-printed multi-stable metamaterials provide valuable contributions to the design of programmable multi-stable metamaterials and their applications in soft robots and intelligent structures. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.