Study on wave dispersion characteristics of piezoelectric sandwich nanoplates considering surface effects

In this study, the wave propagation properties of piezoelectric sandwich nanoplates deposited on an orthotropic viscoelastic foundation are analyzed by considering the surface effects (SEs). The nanoplates are composed of a composite layer reinforced by graphene and two piezoelectric surface layers. Utilizing the modified Halpin-Tsai model, the material parameters of composite layers are obtained. The displacement field is determined by the sinusoidal shear deformation theory (SSDT). The Euler-Lagrange equation is derived by employing Hamilton’s principle and the constitutive equations of piezoelectric layers considering the SEs. Subsequently, the nonlocal strain gradient theory (NSGT) is used to obtain the equations of motion. Next, the effects of scale parameters, graphene distribution, orthotropic viscoelastic foundation, and SEs on the propagation behavior are numerically examined. The results reveal that the wave frequency is a periodic function of the orthotropic angle. Furthermore, the wave frequency increases with the increase in the SEs.

     

Influence of nonlinear spatial distribution of stress and strain on solving problems of solid mechanics

Applied Mathematics and Mechanics - The stress and the strain should be defined as statistical variables averaged over the representative volume elements for any real continuum system. It is shown...     

Surface effect on band structure of magneto-elastic phononic crystal nanoplates subject to magnetic and stress loadings

This paper presents a theoretical model for the size-dependent band structure of magneto-elastic phononic crystal(PC) nanoplates according to the Kirchhoff plate theory and Gurtin-Murdoch theory, in which the surface effect and magneto-elastic coupling are considered. By introducing the nonlinear coupling constitutive relation of magnetostrictive materials, Terfenol-D/epoxy PC nanoplates are carried out as an example to investigate the dependence of the band structure on the surface effect, magn...     

C-13 and H-1 NMR Study of Alkyl and Aryl-Substituted 1-(4′-Dimethylaminobenzylideneamino)pyridinium Perchlorates

C-13 and H-1 NMR spectra of some 1-(4′-dimethylaminobenzylideneamino)pyridinium perchlorates show that the angle of twist of the pyridine ring in unsubstituted, 1, and 2-alkyl substituted compounds 2–5 is comparable. However, it is considerably increased in 2,6-dialkyl derivatives. As seen from the spectral data, pyridine and phenyl rings in 2,6-diphenyl derivative 15 are not coplanar. The effect of 4-alkyl substituent is of hyperconjugative chacter. In general, the amount of the positive charge at C-4 in 2,6-dialkyl substituted salts is higher as compared to 2-monosubstituted compounds.     

基于第一性原理的单层WS2热输运特性研究

二维WS₂是一种层状过渡金属硫化物，因其具有特殊的层状结构、可调带隙及稳定的物理化学性质而备受关注。结合玻尔兹曼输运方程(BTE)和密度泛函理论(DFT),利用第一性原理研究了单层WS₂声子的输运特性，分析了声子的谐性效应和非谐性效应对WS₂晶格热导率的影响机理，计算了其声子的临界平均自由程，提出通过调整阻断频率的方法来调控WS₂的晶格热导率。研究结果表明：单层WS₂在300 K时的本征晶格热导率为149.12 W/(m·K),且随温度的升高而降低；从各声子支对总热导率的贡献来看，声学声子支起主要作用，特别是纵向声学(longitudinal acoustic, LA)声子支对单层WS₂热导率的贡献百分比最大(44.28%);单层WS₂声学声子支和光学声子支之间的较大带隙(声光学声子支之间无散射)导致其具有较高的晶格热导率。本文研究可为基于单层WS₂纳米电子器件的设计和改进提供借鉴和理论指导。     

A Simple Relation between Line Shifts and Atomic Parameters

A comprehensive study of Xe II line shifts (after considering more than 900 transitions) provides the basis for establishing a simple empirical linear relation between the shifts and the inverse of the ionization potential for the er level.     

Slater Sum in Cylindrically Symmetric Inhomogeneous Electron Liquids: Towards A Differential Equation for the Stark Effect in Hydrogen Atom

Abstract

Attention is focussed here on a variety of cylindrically symmetric inhomogeneous electron liquids. These include separable potentials in which a general variation along the (z) axis of cylindrical symmetry is combined with isotropic harmonic confinement in the (x, y) plane. in this case, an explicit differential equation is derived for the Slater sum along the z axis by projecting out of the (off-diagonal) canonical density matrix the states with zero angular momentum about the axis of symmetry. Some attention is then given to the calculation of the Slater sum for a hydrogen-like atom in a uniform electric field of arbitrary strength. the model of a separable potential with harmonic confinement, though no longer exact, is shown to lead directly to a (now approximate) equation for the Slater sum along the z axis for the Stark effect in hydrogen. Finally some further progress is shown to be possible in the extreme high field limit.     

Modeling and testing of snow penetration

Penetration by a cone into snow is commonly used to characterize snow properties. However, the effects of the diameter and half-angle of the cone on the mechanical properties of snow have not been systematically studied. In addition, no estimation of material parameters in a physically-based model has been made such that the results from penetration provide only an index of snow properties. In this paper, modeling and experimental methods are used to examine the effects of cone geometry on the maximum penetration force and associated hardness, with penetrometers ranging from 2.5 to 4 mm in diameter, 15° to 45° in cone half-angle, and testing both fine-grained and coarse-grained snows. The material point method, in conjunction with the Drucker–Prager cap plasticity model, was used to obtain the theoretical penetration force-distance relationship. Global sensitivity studies were conducted that indicate that the cohesion accounts for 86% of the penetration force, followed distantly by friction angle which accounts for 27%. A general trend, for the simulation results was established: for a given half-angle, the penetration force increases with the increase of diameter which holds for most of the test data as well; for a given diameter, the penetration force decreases with the increase of half-angle, which holds for some of the test data. In addition, for a given half-angle, the hardness decreases with the increase of diameter; for a given diameter, the hardness decreases with the increase of half-angle. To take into consideration the uncertainty of test data, a simple interval-based metric was used to compare test data with simulation results; the comparison was satisfactory. The material parameters from the simulations can thus be considered as calibrated ones for the snow studied.     

Contact between two plastically deformable crystals: a discrete dislocation dynamics study

It is customary to simplify the analysis of contact between two elastically deformable bodies by treating an equivalent problem where only one body is deformable and the other is rigid. This is possible provided that the gap geometry and the effective elastic modulus of the bodies in the simplified problem are the same as in the original problem. However, the question arises on whether – and to which extent – the simplification is still valid even when (size-dependent) plasticity occurs. Studies using discrete dislocation plasticity have also, so far, addressed simple contact problems where only one body can deform plastically. Here, we extend the analysis to two bodies in contact that can both deform by dislocation plasticity and investigate under which conditions the response agrees with that of an equivalent simplified problem. The bodies in contact are metal single crystals with sinusoidal and flat surface. It is found that the response of two plastically deformable bodies in contact can be simplified to an equivalent problem where one body is rigid and the other can deform plastically. Also, a plasticity size effect is observed, but the effect fades when the platen becomes more plastically deformable.     

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.