Dynamically control the elastic wave bandgap in wrinkled two-dimensional materials

Elastic wave propagation in finitely deformed layered materials

Compression of a film/substrate bilayer system with different surface/interfacial structures can lead to diverse buckling patterns including sinusoidal wrinkles, ridges, folds, creases and tilted sawteeth wrinkles. In this paper, we show that elastic wave band gaps in the film/substrate bilayer system largely depend on the wrinkling patterns. More interestingly, we find that different wrinkling patterns investigated here can coexist and evolve in one bilayer system and the elastic wave propagation behaviors can be controlled by manipulating the hybrid wrinkling patterns. Our analysis also reveals that the periodic stress pattern plays a dominant role in tuning the bandgap structures in comparison to geometrical patterns caused by surface instability. A careful investigation of the transmission spectra of the composite systems has validated the main findings given by the analysis based on the Bloch wave theory. Potential use of the method and materials reported here to gain wide attenuation frequency ranges and the design of nesting Fibonacci superlattices have been demonstrated.

Using multiple-scattering theory, we investigate the optimization of the elastic wave band gaps of three dimensional three-component phononic crystals with local resonance. The optimum gaps of two systems including Au spheres coated with Pb embedded in Si matrix and Pb spheres coated with plastic embedded in Si matrix are obtained by tuning the ratio of the inner and the outer radii of the coating layers. It also shows that the elastic wave band gaps for the two systems versus the filling fractions and the radius ratio display different features.

Elastic wave and vibration bandgaps in planar square metamaterial-based lattice structures

Active tuning of elastic wave band gaps received significant attention in the recent past. To this end, soft dielectric elastomers (DEs) have indicated great promise owing to their capability to undergo large reversible deformations and deformation-dependent constitutive properties. In this paper, we investigate the longitudinal wave band gaps an infinite periodic soft functionally graded dielectric elastomer subjected to electro-mechanical biasing fields. Material properties of the functionally graded DE are described by the power law. The nonlinear hyperelastic compressible neo–Hookean model is employed for characterizing the constitutive behavior of the soft functionally graded dielectric elastomer. The finite element method with Bloch–Floquet theory is employed for finding the band-structure of the infinitely periodic soft functionally graded DE structure. A parametric study brings out the effect of biasing fields and power law exponent on the band gap characteristics. The biasing mechanical prestress, the electric displacement field show significant influence on position and the width of band gaps. The inferences reported here can find their potential use in the design of soft DE wave devices with tunable band structures.

Bloch wave propagation in finitely stretched soft lattice

Three-dimensional chiral meta-plate lattice structures for broad band vibration suppression and sound absorption

The propagation of elastic waves in one-dimensional (1D) phononic crystals (PCs) withfunctionally graded materials (FGMs) is studied using the spectral finite elements andtransfer matrix methods. FGMs typically treat the graded interlayer as a system of discretelayers, and the material properties are varied according to a well-known rule, such as thepower law. The 1D PCs are composed of both FGMs and isotropic materials, andtheir band gaps can be changed with different FGM compositions and geometryparameters. By selecting the appropriate parameters, the desired filters can bedesigned.

In this paper, the elastic wave band gap characteristics of two-dimensional hard-magnetic soft material phononic crystals (HmSM-PnCs) under the applied magnetic field are studied. Firstly, the relevant material parameters of hard-magnetic soft materials (HmSMs) are obtained by the experimental measurement. Then the finite element model of the programmable HmSM-PnCs is established to calculate its band structure under the applied magnetic field. The effects of some factors such as magnetic field, structure thickness, structure porosity, and magnetic anisotropy encoding mode on the band gap are given. The results show that the start and stop frequencies and band gap width can be tunable by changing the magnetic field. The magnetic anisotropy encoding mode has a remarkable effect on the number of band gaps and the critical magnetic field of band gaps. In addition, the effect of geometric size on PnC structure is also discussed. With the increase of the structure thickness, the start and stop frequencies of the band gap increase.

Band gap materials (i.e. phononic crystals) are the artificially periodic structures, which have the stop band characteristic for elastic waves. The elastic waves will be localized in phononic crystals with defects, which results in the energy being accumulated around the defects. As a result, it is important to analyze the wave propagation and localization in band gap materials, especially for the structures consisting of smart materials. For example, with the mechanical-electro and mechanical-electro-magneto coupling, the phononic crystals consisting of piezoelectric and magnetoelectroelastic materials can be applied widely. This sets the theoretical basis for the design of band gap materials with multi fields coupling. This paper reviews the recent development of the elastic wave propagation and localization in both ordered and disordered band gap materials. The discussion focuses on the stop band and localization characteristics of elastic waves. Analytical methods and important results are also presented. Finally, some problems for further studies are discussed. This work aims to present the basic properties of wave band gaps in phononic crystals and wave localization in disordered periodic structures (e.g. phononic crystals with definite and random defects and phononic quasicrystals).

The paper deals with analysis of the elastic waves in the Reissner‐Mindlin type of plates formed by strongly heterogeneous structures. The homogenized plate model involves frequency‐dependent mass coefficients associated with the plate cross‐section rotations and the plate deflections. Intervals of frequencies called band gaps exist for which these coefficients constituting a mass matrix can be negative, so that certain wave modes cannot propagate. A spectral decomposition based method is proposed which is suitable to compute the plate response for an external loading by periodic forces with frequencies in range of the band gaps. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phononic crystals and acoustic metamaterials hold tremendous potential in controlling mechanical and acoustic waves, thereby enabling remarkable and novel engineering applications such as seismic wave mitigation, impact wave mitigation, elastic cloaking, and acoustic superlens. Given the potential complexity associated with the microstructure of these materials, direct numerical simulation of irregularly shaped and/or large engineering components could be computationally very costly and in many cases prohibitive. Multiscale computational modeling, coupled with model order reduction methodologies present a feasible strategy to simulate the dynamic response of phononic crystals and acoustic metamaterials. In this study, we present the spectral variational multiscale enrichment approach that allows the analysis of a broad range of material microstructures for phononic crystals and acoustic metamaterials. The spectral coarse-scale representation is proposed to capture the salient transient wave phenomena, such as wave dispersion and band gaps that occur in the short wavelength regime. A material phase based model order reduction strategy is devised at the fine-scale. By using the reduced basis for the fine-scale problem, significant numerical efficiency is achieved. Transient elastic wave propagation in two-dimensional phononic crystals and acoustic metamaterials are investigated and the proposed multiscale approach is verified against direct numerical simulations.

Shape optimization of solid–air porous phononic crystal slabs with widest full 3D bandgap for in-plane acoustic waves

Mechanical behavior of single-layer graphdiyne via supersonic micro-projectile impact

Wave propagations exhibit direction and frequency selectivity in two-dimensional (2D) periodic structures, which provides possibilities to regulate wave dispersion and bandgap properties. Most of current researches focus on regulations of 1D waves, and there are few works about active regulations of 2D waves, especially in the structures with strong nonlinearities that have remarkable influences on dispersions. In this work, two types of 2D periodic nonlinear lattice structures with piezoelectric springs, which include a monatomic and a diatomic structure, are designed to implement controllable dispersion and propagation direction of 2D waves. Considering the strong nonlinearities caused by the cubic spring, dynamic models of the wave propagations in the two kinds of periodic structures are established, and an improved incremental harmonic balance (IHB) method is developed to implement efficient and accurate calculations of the 2D wave propagation. Influences of active and structural parameters on dispersion and bandgap properties are comprehensively studied, and the regulation ability of the piezoelectric springs is demonstrated where the proportional voltage constant is the active control parameter with particle displacements as the feedback. Results also show that a piezoelectric modulated bandgap and a critical wave vector region are created by positive and negative proportional constants, respectively, which indicate that the structures can be used to filter a wide range of low-frequency long-wavelength noises and waves at particular directions. The properties predicted by the improved IHB method are verified by numerical experiments.