Size effect of the elastic modulus of rectangular nanobeams:Surface elasticity effect

The size-dependent elastic property of rectangular nanobeams （nanowires or nanoplates） induced by the surface elas- ticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 1 O0 nm. It is also found that the theoretical results calculated by a mod- ified core-shell model have more obvious advantages than those by other models （core-shell model and core-surface model） by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers.

An automatic compensation method on compression effect and surface elasticity measurement based on the deflection signal of AFM

Atomic force microscope （AFM）, as an important instrument in micro/nano operation, has been widely used to measure sampie＇s height information. However, the so called compression effect, due to force aroused from the contact of AFM tip with a sample surface, would result in imprecision of the surface＇s height measurement, i.e., the measured height is lower than expected. Up to now, there is not any effective and rapid method to attenuate this kind of measurement error. Thus, in this paper, an algorithm to obtain high accurate height measurement is proposed. Firstly, the concept of force curve is used to analyze the basic principle of the compression effect. Secondly, an automatic compensation method by fusing the height signal and the deflection signal is proposed. The proposed algorithm can also be used to obtain a surface elasticity image. Finally, in order to validate the proposed method, two experiments are conducted with respect to mufti-wall nano-carbon tubes on a silicon substrate and graphemes on a mica substrate.

Nano-Contact Problem with Surface Effects on Triangle Distribution Loading

This work presents a theoretical study of contact problem. The Fourier integral transform method based on the surface elasticity theory is adopted to derive the fundamental solution for the contact problem with surface effects, in which both the surface tension and the surface elasticity are considered. As a special case, the deformation induced by a triangle distribution force is discussed in detail. The results are compared with those of the classical contact problem. At nano-scale, the contributions of the surface tension and the surface elasticity to the stress and displacement are not equal at the contact surface. The surface tension plays a major role to the normal stress, whereas the shear stress is mainly affected by the surface elasticity. In addition, the hardness of material depends strongly on the surface effects. This study is helpful to characterize and measure the mechanical properties of soft materials through nanoindentation.

Dynamic analysis of elastic screen surface with multiple attached substructures and experimental validation

A feasible method to improve the reliability and processing efficiency of large vibrating screen via the application of an elastic screen surface with multiple attached substructures （ESSMAS） was proposed. In the ESSMAS, every screen rod, with ends embedded into elastomer, is coupled to the main screen structure in a relatively flexible manner. The theoretical analysis was conducted, which consists of establishing dynamic model promoted from the fuzzy structure theory as well as calculating for the equivalent stiffness of each attached structure. According to the numerical simulation using the NEWMARK-fl integration method, this assembling pattern significantly leads to the screen surface/rod having larger vibration intensity than that of the corresponding position on screen structure, which specifically, with an averaged acceleration amplitude increasing ratio of 11.37% in theoretical analysis and 20.27% in experimental test. The experimental results, within a tolerant error, also confirm the established model and demonstrate the feasibility of ESSMAS.

Dynamic analysis of new type elastic screen surface with multi degree of freedom and experimental validation

A feasible method was proposed to improve the vibration intensity of screen surface via application of a new type elastic screen surface with multi degree of freedom(NTESSMDF). In the NTESSMDF, the primary robs were coupled to the main screen structure with ends embedded into the elastomers, and the secondary robs were attached to adjacent two primary robs with elastic bands. The dynamic model of vibrating screen with NTESSMDF was established based on Lagrange's equation and the equivalent stiffnesses of the elastomer and elastic band were calculated. According to numerical simulation using the 4th order Runge-Kutta method, the vibration intensity of screen surface can be enhanced substantially with an averaged acceleration amplitude increasing ratio of 72.36%. The primary robs and secondary robs vibrate inversely in steady state, which would result in the friability of materials and avoid stoppage. The experimental results validate the dynamic characteristics with acceleration amplitude rising by62.93% on average, which demonstrates the feasibility of NTESSMDF.

METHOD TO SOLVE ELASTIC CONJUGATE SURFACES IN MULTI-TEETH MESHING

A method to solve the elastic conjugate surfaces in multi-teeth meshing ispresented. In mechanical manufacturing and design, there exist a lot of problems relating toconjugate surfaces, such as three-dimensional engagement, steel rolling and workpiece machining,which cause great effects on the quality of machining and performances of transmission. This methoddescribes relation between conjugate motion and elastic deformation in the process of mesh-in andmesh-out, and can be used to determine the profile of gear tooth by a certain given load sharing.

Defect-free surface of quartz glass polished in elastic mode by chemical impact reaction

Removal of brittle materials in the brittle or ductile mode inevitably causes damaged or strained surface layers containing cracks, scratches or dislocations. Within elastic deformation, the arrangement of each atom can be recovered back to its original position without any defects introduced. Based on surface hydroxylation and chemisorption theory, material removal mechanism of quartz glass in the elastic mode is analyzed to obtain defect-free surface. Elastic contact condition between nanoparticle and quartz glass surface is confirmed from the Hertz contact theory model. Atoms on the quartz glass surface are removed by chemical bond generated by impact reaction in the elastic mode, so no defects are generated without mechanical process. Experiment was conducted on a numerically controlled system for nanoparticle jet polishing, and one flat quartz glass was polished in the elastic mode. Results show that scratches on the sample surface are completely removed away with no mechanical defects introduced, and microroughness(Ra) is decreased from 1.23 nm to 0.47 nm. Functional group Ce — O — Si on ceria nanoparticles after polishing was detected directly and indirectly by FTIR, XRD and XPS spectra analysis from which the chemical impact reaction is validated.

Photodetachment of H^-near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H- near an elastic wall in a magnetic field. The magnetic field confines the perpendicular motion of the electron, which results in a real three-dimensional well for the detached electron. The analytical formulas for the cross section of the photodetachment in the three-dimensional quantum well are derived based on both the quantum approach and closed-orbit theory. The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment. The oscillation amplitude depends on the strength of the magnetic field, the ion-wall distance and the photon polarization as well. Specially, for the circularly polarized photon-induced photodetachment, the cross sections display a suppressed （E - Eth）1/2 threshold law with energy E in the vicinity above Landau energy Eta, contrasting with the （E - Eta）-1/2 threshold law in the presence of only the magnetic field. The semiclassical calculation fits the quantum result quite well, although there are still small deviations. The difference is attributed to the failure of semiclassical mechanics.

Nonlinear Thermal Buoyancy on Ferromagnetic Liquid Stream Over a Radiated Elastic Surface with Non Fourier Heat Flux

The current article discusses the heat transfer characteristics of ferromagnetic liquid over an elastic surface with the thermal radiation and non-Fourier heat flux.In most of the existing studies,the heat flux is considered as constant,but whereas we incorporated the non-Fourier flux to get the exact performance of the flow.Also,we excluded the PWT and PHF cases to control the boundary layer of the flow.The governing equations related to our contemplate are changed into non-linear ordinary differential equations(ODE’s)by utilizing appropriate similarity changes,which are at the point enlightened by Runge–Kutta based shooting approach.The equations are broken down concerning boundary conditions and to be explained prescribed wall temperature(PWT)and prescribed heat flux(PHF)cases.The impacts of diverse non-dimensional physical parameters on velocity and temperature profiles are laid out graphically.Also,the assortment of skin friction and local Nusselt number for both PWT and PHF cases for various assessments of non-dimensional parameters have been sorted out.Towards the wrap-up of the examination,we suspect that the friction factor coefficient is higher in the PWT case compared to the PHF case.This result helps to conclude that the flux conditions are useful for cooling applications.

Approximate Tangent Plane Method for Calculating Surface Deformation in Elastic Contact Problems

A flew numerical method for constructing a pressure distribution to calculate surface elastic deformationcaused by normal contact pressure is developed in this paper. The pressure distribution over one of nonequidistantrectangles is fitted by an approximate tangent plane(ATP), which is formed by five pressure samples. Because thepressure distribution could be expressed as an one order linear polynomial, the iterative expression of elasticdeformation deduced by this method is simple, and the numerical accuracy is higher.

Analytical Solutions for an Isotropic Elastic Half-Plane with Complete Surface Effects Subjected to a Concentrated/Uniform Surface Load

Within the context of Gurtin-Murdoch surface elasticity theory,closed-form analytical solutions are derived for an isotropic elastic half-plane subjected to a concentrated/uniform surface load.Both the effects of residual surface stress and surface elasticity are included.Airy stress function method and Fourier integral transform technique are used.The solutions are provided in a compact manner that can easily reduce to special situations that take into account either one surface effect or none at all.Numerical results indicate that surface effects generally lower the stress levels and smooth the deformation profiles in the half-plane.Surface elasticity plays a dominant role in the in-plane elastic fields for a tangentially loaded half-plane,while the effect of residual surface stress is fundamentally crucial for the out-of-plane stress and displacement when the half-plane is normally loaded.In the remaining situations,combined effects of surface elasticity and residual surface stress should be considered.The results for a concentrated surface force serve essentially as fundamental solutions of the Flamant and the half-plane Cerruti problems with surface effects.The solutions presented in this work may be helpful for understanding the contact behaviors between solids at the nanoscale.

Surface Elastic Effects on Electromechanical Responses of a Piezoelectric Semiconducting Nanobeam

Piezoelectric semiconductors(PSCs)find extensive applications in modern smart electronic devices because of their dual properties of being piezoelectric and semiconductive.With the increasing demand for miniaturization of these devices,the performance of their components needs to be carefully designed and optimized,especially when reduced to nanosize.It has been shown that surface elastic properties play a substantial role in the mechanical performance of nanoscale materials and structures.Building on this understanding,the surface elastic effects,encompassing surface residual stress,surface membrane stiffness,and surface bending stiffness,are comprehensively taken into account to explore the electromechanical responses of a PSC nanobeam.Additionally,the flexoelectric effect on their responses is also systematically studied.The results of this work reveal that surface elastic properties predominantly influence mechanical performance,while the flexoelectric effect plays a more dominant role in electric-related quantities at the nanoscale.Notably,the significance of surface bending rigidity,which was often underestimated in the earlier literature,is demonstrated.Furthermore,owing to the flexoelectric effect,the linear distribution of electric potential and charge carriers along the length transforms into a nonlinear pattern.The distributions of electric potential and charge carriers across the cross section are also evidently impacted.Moreover,the size-dependent responses are evaluated.Our findings may provide valuable insights for optimizing electronic devices based on nanoscale PSCs.

A review on the application of modified continuum models in modeling and simulation of nanostructures

Analysis of the mechanical behavior of nanos- tructures has been very challenging. Surface energy and non- local elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams, graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are men- tioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomateri- als are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires fur- ther applications of modified continuum models in modeling nanomaterials and nanostructures.

Elastic fields around a nanosized elliptic hole in decagonal quasicrystals

Based on the variational principle, a continuum theory of surface elasticity and new boundary conditions for qua- sicrystals is proposed. The effect of the residual surface stress on a decagonal quasicrystal that is weakened by a nanoscale elliptical hole is considered. The explicit expressions for the hoop stress along the edge of the hole are obtained using the Stroh formalism. The results show that the residual surface stress and the shape of the hole have a significant effect on the elastic state around the hole.

Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching

A model for the mechanics of woven fabrics is developed in the framework of two-dimensional elastic surface theory. Thickness effects are modeled indirectly in terms of appropriate constitutive equations. The model accounts for the strain of the fabric and additional effects associated with the normal bending, geodesic bending, and twisting of the constituent fibers.

Three-dimensionally nonlocal tensile nanobars incorporating surface effect: A self-consistent variational and well-posed model

A naturally discrete nanobar implies that the continuum axiom fails, and the surface-to-volume ratio is very large. The nonlocal theory of elasticity releasing the continuum axiom and the surface theory of elasticity are therefore employed to model tensile nanobars in this work. As commonly believed in the current practice, the axial nonlocal effect is only taken into account to analyze the mechanical behaviors of nanobars, regardless of the three-dimensional inherent atomistic interactions. In this study,a three-dimensional nonlocal constitutive law is developed to model the true nonlocal effect of nanobars, and based on which,a self-consistent variational bar model is proposed. It has been revealed for the first time how both the cross-sectional nonlocal interactions and the axial nonlocality affect the tensile behaviors of nanobars. It is found that the nonlocal influence predicted by the currently axial nonlocal bar model is grossly underestimated. Both the nonlocal cross-sectional and axial interactions become significant when the length-to-height ratio of nanobars is small. If the length-to-height ratio is relatively large(slender bars), the main nonlocal effect stems, however, from the nonlocal cross-sectional effect, rather than the axial nonlocal effect. This work also shows that it is possible to overcome the ill-posed problem of the pure nonlocal integral elasticity by employing both the pure nonlocal integral elasticity and surface elasticity. A well-posed size-dependent governing equation has been established for modeling nanobars under tension, and closed-form solutions are derived for their displacements. Based on the closed-form solutions, the effective elastic modulus is obtained and will be useful for calibrating the physical quantities in the "discretecontinuum" transition region for a span-scale modeling approach. It is shown that the effective elastic modulus may be softening or hardening, depending on the competition between the surface(modulus-hardening) and nonlocal(modulus-softening) effects.

Towards Understanding Why the Thin Membrane Transducer Deforms:Surface Stress-Induced Buckling

This study is directed towards a comprehensive exploration on the deformation mechanism of the thin membrane transducer（TMT） caused by surface stress variation.We stress that the biomolecular interaction has changed the magnitude of the surface stress;and when the surface stress exceeds a critical value the TMT will buckle and deform.Based upon Gurtin＇s theory of surface elasticity and principle of finite deformation,we abstract the TMT as a nanobeam with two clamped ends,and the close-formed governing equation set is derived accordingly.A computer code via the shooting method is developed to solve the presented two-point boundary value problem.In succession,the nanobeam deflection and critical parameters for buckling are quantitatively discussed.This investigation lays the theoretical foundation of TMTs;and it is also beneficial to gain deep insight into characterizing mechanical properties of nanomaterials and engineering nano-devices.

Collisionless tool orientation smoothing above blade stream surface using NURBS envelope

In five-axis machining,tool orientation above a blade stream surface may lead to tool collision and a decrease in workpiece rigidity.Hence,collisionless tool orientation smoothing(TOS)becomes an important issue.On the basis of a constant scallop height tool path,the triangular facets in the faces,vertices format are constructed from cutter contact(CC)using the Voronoi incremental algorithm.The cutter location(CL)points candidate set is represented by an oblique elliptic cone whose vertex lies at CC using NURBS envelope.Whether the CL point is above its CC is judged by the dot product between the normal vector and the point on triangulation nearest to the CL point.The curvatures at CC are obtained by fitting a moving least square(MLS) quadratic patch to the local neighborhood of a vertex and calculating eigenvectors and eigenvalues of the Hessian matrix.Triangular surface elastic energy is employed as the weight in selection from the NURBS envelope.The collision is judged by NURBS surface intersection.TOS can then be expressed by selecting a CL point for each CC point and converted into a numerical control(NC)code automatically according to the postprocessor type of the machine center.The proposed method is verified by finishing of a cryogenic turboexpander impeller of air separation equipment.

Nonlinear Vibration of the Flexoelectric Nanoplate with Surface Elastic Electrodes Under Active Electric Loading

This paper mainly studies the effects of surface elastic electrodes and electric loading on the nonlinear vibration of flexoelectric nanoplate.The governing equations are derived based on the von Karman type strain-displacement relations and the flexoelectricity theory.The nonlinear vibration equation is solved by an approximate method.Numerical results reveal that the surface elastic electrodes and the length-width ratio of flexoelectric nanoplate have a more significant effect on the nonlinear resonant frequency of simply-supported nanoplate than that of the all-edge-clamped nanoplate.Meanwhile,the effect of the graphene electrode on the nonlinear resonant frequency is more notable than that of the A1 electrode.Additionally,the applied electric loading can significantly affect the nonlinear resonant frequency of the flexoelectric nanoplate.For the nanoplates with different boundary conditions,the applied electric loading has different effects on the nonlinear resonant frequency.This study has certain research significance in the structure design and examination of the flexoelectric nanoplate with electrodes.

Elastic wave scattering from rough free surfaces of solids

Elastic wave scattering by a rough free surface of solids is analyzed. The analysis is based on the concept of scattering amplitude (SA) and perturbation approximation. The SA method is very convenient for rough surface scattering problems. By solving the boundary equations, the first and the second order solutions of approximate scattering amplitude are obtained. The general solutions are used for, as an example, the wave scattering by rough surfaces with Gaussian distribution. The mean field and variance are given. Finally, an experiment is designed to verify the theoretical predications.