Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects

The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are derived.An electro-elastic model is developed to investigate the anti-plane strain problem of Love wave propagation.By introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated problems.Satisfying the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary conditions.Numerical examples are given to reveal the effects of the boundary conditions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.

Analytic solution of quasicrystal microsphere considering the thermoelectric effect and surface effect in the elastic matrix

The incorporation of the quasicrystalline phase into the metal matrix offers a wide range of potential applications in particle-reinforced metal-matrix composites.The analytic solution of the piezoelectric quasicrystal(QC)microsphere considering the thermoelectric effect and surface effect contained in the elastic matrix is presented in this study.The governing equations for the QC microsphere in the matrix subject to the external electric loading are derived based on the nonlocal elastic theory,electro-elastic interface theory,and eigenvalue method.A comparison between the existing results and the finite-element simulation validates the present approach.Numerical examples reveal the effects of temperature variation,nonlocal parameters,surface properties,elastic coefficients,and phason coefficients on the phonon,phason,and electric fields.The results indicate that the QC microsphere enhances the mechanical properties of the matrix.The results are useful for the design and understanding of the characterization of QCs in micro-structures.

Investigation of the Interaction Between the Free Surface and A Semi/Shallowly Submerged Underwater Vehicle

The present study aims to investigate the interaction between the free surface and a semi/shallowly submerged underwater vehicle,especially when the submergence depth h is smaller than 0.75D(D:submarine maximum diameter).In this respect,the straight-ahead simulations of the generic SUBOFF underwater vehicle geometry are conducted with constant forward velocities using the Unsteady Reynolds-Averaged Navier-Stokes(URANS)equations with a Shear-Stress Transport(SST)k-ωturbulence model in commercial code Fluent,at submergence depths and Froude numbers ranging from h=0 to h=3.3D and from Fn=0.205 to Fn=0.512,respectively.The numerical models are verified against the existing experimental data.The analysis of the obtained results indicates that in the case of the semi and shallowly submerged underwater vehicle(UV),both the submergence depth and forward velocity have a great effect on the behaviors of hydrodynamic forces acting on the UV.The magnitude of maximum total resistance may reach almost five times the value of resistance exerted on the totally submerged hull.Both the forces acting on the UV and the generated waves when the submergence depth h is smaller than 0.75D are significantly different from those whenr h is larger than 0.75D.The conclusions can be used as reference for future research on near free surface motions of underwater vehicles and the design of small water-plane area twin hull.

Surface effects on a mode-III reinforced nano-elliptical hole embedded in one-dimensional hexagonal piezoelectric quasicrystals

To effectively reduce the field concentration around a hole or crack,an anti-plane shear problem of a nano-elliptical hole or a nano-crack pasting a reinforcement layer in a one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)is investigated subject to remotely mechanical and electrical loadings.The surface effect and dielectric characteristics inside the hole are considered for actuality.By utilizing the technique of conformal mapping and the complex variable method,the phonon stresses,phason stresses,and electric displacements in the matrix and reinforcement layer are exactly derived under both electrically permeable and impermeable boundary conditions.Three size-dependent field intensity factors near the nano-crack tip are further obtained when the nano-elliptical hole is reduced to the nano-crack.Numerical examples are illustrated to show the effects of material properties of the surface layer and reinforced layer,the aspect ratio of the hole,and the thickness of the reinforcing layer on the field concentration of the nano-elliptical hole and the field intensity factors near the nano-crack tip.The results indicate that the properties of the surface layer and reinforcement layer and the electrical boundary conditions have great effects on the field concentration of the nano-hole and nano-crack,which are useful for optimizing and designing the microdevices by PQC nanocomposites in engineering practice.

Surface-effects-dominated thermal and mechanical responses of zinc oxide nanobelts

t Molecular dynamics （MD） simulations are carried out to characterize the mechanical and thermal responses of [011^-1]-oriented ZnO nanobelts with lateral dimensions of 21.22A × 18.95 A, 31.02A× 29.42 A, and40.81A ×39.89A over the temperature range of 300-1000 K. The Young＇s modulus and thermal conductivity of the nanobelts are evaluated. Significant surface effects on properties due to the highsurface-to-volume ratios of the nanobelts are observed. For the mechanical response, surface-stress-induced internal stress plays an important role. For the thermal response, surface scattering of phonons dominates. Calculations show that the Young＇s modulus is higher than the corresponding value for bulk ZnO and decreases by -33% as the lateral dimensions increase from 21.22 A × 18.95A to 40.81 A × 39.89A. The thermal conductivity is one order of magnitude lower than the corresponding value for bulk ZnO single crystal and decreases with wire size. Specifically, the conductivity of the 21.22 A × 18.95 A belt is approximately （31-18）% lower than that of the 40.81 A × 39.89 A belt over the temperature range analyzed. A significant dependence of properties on temperature is also observed, with the Young＇s modulus decreasing on average by 12% and the conductivity decreasing by 50% as temperature increases from 300 K to 1000 K.

Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage

A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.

Effect of surface stress and surface-induced stress on behavior of piezoelectric nanobeam

A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlin- ear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Com- pared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However~ the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models Mso have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam.

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions： hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.

Effects of surface adsorbed oxygen, applied voltage, and temperature on UV photoresponse of ZnO nanorods

The ultraviolet（UV） photoresponses of ZnO nanorods directly grown on and between two micro Au-electrodes by using electric-field-assisted wet chemical method are measured comprehensively under different conditions, including ambient environment, applied bias voltage, gate voltage and temperature. Experimental results indicate that the photoresponses of the ZnO nanorods can be modulated by surface oxygen adsorptions, applied voltages, as well as temperatures. A model taking into account both surface adsorbed oxygen and electron-hole activities inside ZnO nanorods is proposed. The enhancement effect of the bias voltage on photoresponse is also analyzed. Experimental results shows that the UV response time（to 63%） of ZnO nanorods in air and at 59°C could be shortened from 34.8 s to 0.24 s with a bias of 4 V applied between anode and cathode.

Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model

This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton＇s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

Surface effect of nanocrystals doped with rare-earth ions enriched on surface and its application in upconversion luminescence

By employing a certain proportion of hydrogen peroxide, ammonia, ammonium fluoride, and ethylene diamine tetraacetic acid （EDTA） as precipitator, well-crystallized LaOF：Eu3＋ and LaOF：Yba＋, Era＋ nanocrystals are synthe- sized by using the chemical co-precipitation method. The structural properties of these samples are characterized by X-ray diffraction （XRD）, transmission electron microscopy （TEM）, and Fourier transform infrared spectroscopy （FTIR） spectra. The results show that all the samples have an average size below 70 nm, which decreases gradually with the increase of the EDTA content, and a certain number of EDTA molecules are coupled with doped ions on the surfaces of nanocrystals. Most of the doped ions are proved to be enriched on the surfaces of nanocrystals and surrounded by the high energy vibration groups and bonds in EDTA molecules. The observed differences in upconversion emission spectrum among the different LaOF：Yba＋, Er3＋ nanocrystals are explained by the different two-photon upconversion mechanisms. Especially, in the LaOF：Yba＋, Era＋ nanocrystals with EDTA, the two-photon processes that contain several special cross-relaxation processes are introduced to analyse the corresponding upconversion mechanisms.

Bending of functionally graded nanobeams incorporating surface effects based on Timoshenko beam model

The bending responses of functionally graded （FG） nanobeams with simply supported edges are investigated based on Timoshenko beam theory in this article. The Gurtin-Murdoch surface elasticity theory is adopted to analyze the influences of surface stress on bending response of FG nanobeam. The material properties are assumed to vary along the thickness of FG nanobeam in power law. The bending governing equations are derived by using the minimum total potential energy principle and explicit formulas are derived for rotation angle and deflection of nanobeams with surface effects. Illustrative examples are implemented to give the bending deformation of FG nanobeam. The influences of the aspect ratio, gradient index, and surface stress on dimensionless deflection are discussed in detail.

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.

Surface effects on mechanical behavior of elastic nanoporous materials under high strain

This paper studies surface effects on the mechanical behavior of nanoporous materials under high strains with an improved anisotropic Kelvin model. The stress-strain relations are derived by the theories of Euler-Bernoulli beam and surface elasticity. Mean- while, the influence of strut （or ligament） size on the mechanical properties of nanoporous materials is discussed, which becomes a key factor with consideration of the residual sur- face stress and the surface elasticity. The results show that the decrease in the strut diameter and the increase in the residual surface stress or the surface elasticity can both lead to an increase in the carrying capacity of nanoporous materials. F^lrthermore, me- chanical behaviors of anisotropic nanoporous materials in different directions （the rise direction and the transverse direction） are investigated. The results indicate that the sur- face effects in the transverse direction are more obvious than those in the rise direction for anisotropic nanoporous materials. In addition, the present results can be reduced to the cases of conventional foams as the strut size increases to micron-scale, which confirms validity of the model to a certain extent.

Propagation of Rayleigh-type surface waves in a layered piezoelectric nanostructure with surface effects

This work investigates the dispersion properties of Rayleigh-type surface waves propagating in a layered piezoelectric nanostructure composed of a piezoelectric nanofilm over an elastic substrate.As one of the most important features of nanostructures,surface effects characterized by surface stresses and surface electric displacements are taken into account through the surface piezoelectricity theory and the nonclassical mechanical and electrical boundary conditions.Concrete expressions of the dispersion equation are derived,and numerical results are provided to examine the effects of several surface-related parameters,including the surface elasticity,surface piezoelectricity,surface dielectricity,surface density,as well as surface residual stress,on the dispersion modes and phase velocity.The size-dependent dispersion behaviors occurring with surface effects are also predicted,and they may vanish once the thickness of the piezoelectric nanofilm reaches a critical value.

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,magnetic field,pre-stress,and geometric parameters.The results show that the surface effect has promotive influence on dispersion curves of the band structure,and the band gaps can be improved gradually with the increase in the material intrinsic length.Meanwhile,the band gaps exhibit obvious nonlinear coupling characteristics owing to the competition between the magnetic field and the pre-stress.By considering the surface effect and magneto-elastic coupling,the open and closed points of band gaps are found when the lattice constant to thickness ratio increases.The study may provide a method for flexible tunability of elastic wave propagation in magneto-elastic PC nanoplates and functional design of highperformance nanoplate-based devices.

Curved surface effect and emission on silicon nanostructures

The curved surface （CS） effect on nanosilicon plays a main role in the activation for emission and photonic manipulation. The CS effect breaks the symmetrical shape of nanosilicon on which some bonds can produce localized electron states in the band gap. The investigation in calculation and experiment demonstrates that the different curvatures can form the characteristic electron states for some special bonding on the nanosilicon surface, which are related to a series of peaks in photoluminecience （PL）, such as LN, LNO, Lo1, and Lo2 lines in PL spectra due to Si-N, Si-NO, Si=O, and Si-O-Si bonds on curved surface, respectively. Si-Yb bond on curved surface of Si nanostructures can provide the localized states in the band gap deeply and manipulate the emission wavelength into the window of optical communication by the CS effect, which is marked as the Lyb line of electroluminescence （EL） emission.

Influences of surface effects and large deformation on the resonant properties of ultrathin silicon nanocantilevers

The purpose of the present work is to quantify the influences of the discrete nature, the surface effects, and the large deformation on the bending resonant properties of long and ultrathin （100） silicon nanocantilevers. We accomplish this by using an analytical semi-continuum Keating model within the framework of nonlinear, finite deformation kinematics. The semi-continuum model shows that the elastic behaviors of the silicon nanocantilevers are size-dependent and surface- dependent, which agrees well with the molecular dynamics results. It also indicates that the dominant effect on the fundamental resonant frequency shift of the silicon nanocantilever is adsorption-induced surface stress, followed by the discrete nature and surface reconstruction, whereas surface relaxation has the least effect. In particular, it is found that a large deformation tends to increase the nonlinear fundamental frequency of the silicon nanocantilever, depending not only on its size but also on the surface effects. Finally, the resonant frequency shifts due to the adsorption-induced surface stress predicted by the current model are quantitatively compared with those obtained from the experimental measurement and the other existing approach. It is noticed that the length-to-thickness ratio is the key parameter that correlates the deviations in the resonant frequencies predicted from the current model and the empirical formula.

Frequency equations of nonlocal elastic micro/nanobeams with the consideration of the surface effects

A nonlocal elastic micro/nanobeam is theoretically modeled with the consideration of the surface elasticity, the residual surface stress, and the rotatory inertia,in which the nonlocal and surface effects are considered. Three types of boundary conditions, i.e., hinged-hinged, clamped-clamped, and clamped-hinged ends, are examined. For a hinged-hinged beam, an exact and explicit natural frequency equation is derived based on the established mathematical model. The Fredholm integral equation is adopted to deduce the approximate fundamental frequency equations for the clamped-clamped and clamped-hinged beams. In sum, the explicit frequency equations for the micro/nanobeam under three types of boundary conditions are proposed to reveal the dependence of the natural frequency on the effects of the nonlocal elasticity, the surface elasticity, the residual surface stress, and the rotatory inertia, providing a more convenient means in comparison with numerical computations.