Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map

In this paper, a method based on the Dirichlet- to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann （DtN） map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acoustic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.

Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory

In this paper, the free vibration of magneto- electro-elastic （MEE） nanoplates is investigated based on the nonlocal theory and Kirchhoff plate theory. The MEE nanoplate is assumed as all edges simply supported rectan gular plate subjected to the biaxial force, external electric potential, external magnetic potential, and temperature rise. By using the Hamilton＇s principle, the governing equations and boundary conditions are derived and then solved analytically to obtain the natural frequencies of MEE nanoplates. A parametric study is presented to examine the effect of the nonlocal parameter, thermo-magneto-electro-mechanical loadings and aspect ratio on the vibration characteristics of MEE nanoplates. It is found that the natural frequency is quite sensitive to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the thermal loading.

A High-Temperature β-Phase NaMnO2 Stabilized by Cu Doping and Its Na Storage Properties

The high-temperature β-phase NaMnO2 is a promising material for Na-ion batteries（NIBs） due to its high capacity and abundant resources. However, the synthesis of phase-pure -NaMnO2 is burdensome and costineffective because it needs to be sintered under oxygen atmosphere at high temperature and followed by a quenching procedure. Here we first report that the pure β phase can be stabilized by Cu-doping and easily synthesized by replacing a proportion of Mn with Cu via a simplified process including sintering in air and cooling to room temperature naturally. Based on the first-principle calculations, the band gap decreases from 0.7 eV to 0.3 eV, which indicates that the electronic conductivity can be improved by Cu-doping. The designed -NaCu（0.1）Mn（0.9）O2 is applied as cathode in NIBs, exhibiting an energy density of 419 Wh/kg and better performance in terms of rate capability and cycling stability than those in the undoped case.

Buckling and post-buckling analyses of size-dependent piezoelectric nanoplates

This paper attempts to investigate the buckling and post-buckling behaviors of piezoelectric nanoplate based on the nonlocal Mindlin plate model and yon Karman geometric nonlinearity. An external electric voltage and a uniform temperature rise are applied on the piezoelectric nanoplate. Both the uniaxial and biaxial mechanical compression forces will be considered in the buckling and post-buckling analysis. By substituting the energy functions into the equation of the minimum total potential energy principle, the governing equations are derived directly, and then discretized through the differential quadrature （DQ） method. The buckling and post-buckling responses of piezoelectric nanoplates are calculated by employing a direct iterative method under different boundary conditions. The numerical results are presented to show the influences of different factors including the nonlocal parameter, electric voltage, and temperature rise on the buckling and post-buckling responses.

The axisymmetric torsional contact problem of a functionally graded piezoelectric coated half-space

In this article, we study the axisymmetric torsional contact problem of a half-space coated with functionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thickness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral transform technique and reduce the problem to a singular integral equation, and then numerically determine the unknown contact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.

Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer

The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally graded layer arbitrarily vary with depth,and the foundation is assumed to be elastic,yet much harder than a layer.Approximated analytical solution is constructed,and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem.Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties.Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.

Active feedback control of sound radiation in elastic wave metamaterials immersed in water with fluid-solid coupling

Due to their potential properties unlike traditional materials and structures,elastic wave metamaterials have received significant interests in recent years.With the coupling between the acoustic and vibration,their mechanical characteristics can be tuned by the active feedback control system at low frequency ranges in which the traditional passive control is limited.This work illustrates that the superior performances of the effective mass density and sound pressure level(SPL)of an elastic wave metamaterial can be significantly changed by the active control,in which the periodic array of local resonators and orthogonal stiffeners are included.Significantly,based on the locally resonant mechanism,the negative density occurs over a frequency range.Due to the effects of lattice constant,structural damping and other parameters,the SPL with the function of fluid-solid coupling are illustrated and discussed.

Sound Transmission Comparisons of Active Elastic Wave Metamaterial Immersed in External Mean Flow

Using the active feedback control system on the elastic wave metamaterial,this research concentrates on the sound transmission with the dynamic effective model.The metamaterial is subjected to an incident pressure and immersed in the external mean flow.The elastic wave metamaterial consists of double plates and the upper and lower four-link mechanisms are attached inside.The vertical resonator is attached by the active feedback control system and connected with two four-link mechanisms.Based on the dynamic equivalent method,the metamaterial is equivalent as a single-layer plate by the dynamic effective parameter.With the coupling between the fluid and structure,the expression of the sound transmission loss(STL)is derived.This research shows the influence of effective mass density on sound transmission properties,and the STL in both modes can be tuned by the acceleration and displacement feedback constants.In addition,the dynamic response and the STL are also changed obviously by different values of structural damping,incident angle(i.e.,the elevation and azimuth angles)and Mach number of the external fluid with the mean flow property.The results for sound transmission by two methods are compared,i.e.,the virtual work principle for double plates and the dynamic equivalent method corresponding to a single one.This paper is expected to be helpful for understanding the sound transmission properties of both pure single-and double-plate models.

Propagation of flexural waves in phononic crystal thin plates with linear defects

The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.

Molecular Dynamics Simulations of the Orientation Effect on the Initial Plastic Deformation of Magnesium Single Crystals

Molecular dynamics simulation is employed to study the tension and compression deformation behaviors of magnesium single crystals with different orientations.The angle between the loading axis and the basal direction ranges from 0° to 90°.The simulation results show that the initial defects usually nucleate at free surfaces,but the initial plastic deformation and the subsequent microstructural evolutions are various due to different loading directions.The tension simulations exhibit the deformation mechanisms of twinning,slip,crystallographic reorientation and basal/prismatic transformation.The twinning,crystallographic reorientation and basal/prismatic transformation can only appear in the crystal model loaded along or near the a-axis or c-axis.For the compression simulations,the basal,prismatic and pyramidal slips are responsible for the initial plasticity,and no twinning is observed.Moreover,the plastic deformation models affect the yield strengths for the samples with different orientations.The maximum yield stresses for the samples loaded along the c-axis or a-axis are much higher than those loaded in other directions.

Extreme transmission of elastic metasurface for deep subwavelength focusing

In this paper,elastic metasurfaces composed of zigzag units are proposed to manipulate flexural waves at a deep subwavelength scale.Through the parameter optimization of the genetic algorithm,units with full transmission and full phase control can be found,while the width is only one-fifth of the wavelength.The outstanding capability of the units is explained by analyzing.their wave fields.The flat and the curved metasurfaces for focusing are designed and simulated,showing excellent performance.Experimental results of the flat metasurface show that the incident wave energy at the focal point is enhanced over 6 times,verifying the simulation results.The proposed metasurfaces could be useful in the design of.compact and efficient elastic devices.

Band structure properties of elastic waves propagating in the nanoscaled nearly periodic layered phononic crystals

The localization factor is used to describe the band structures for P wave propagating normally in the nanoscaled nearly periodic layered phononic crystals. The localization factor is calculated by the transfer matrix method based on the nonlocal elastic continuum theory.Three kinds of nearly periodic arrangements are concerned, i.e., random disorder, quasiperiodicity and defects. The influences of randomly disordered degree of the sub-layer＇s thickness and mass density, the arrangement of quasi-periodicity and the location of defect on the band structures and cut-off frequency are analyzed in detail.