Nonlocal Surface Research Articles

Dynamic modeling of embedded curved nanobeams incorporating surface effects

To investigate the surface effects on vibration of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension and surface density for modeling the nano scale effect. The governing equations are determined via the energy method. An-alytically Navier method is utilized to solve the governing equations for simply supported at both ends. Solving these equations enables us to estimate the natural frequency for circular curved nanobeam including Winkler and Pasternak elastic foundations. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations and opening angle of circular curved nanobeam on the natural frequency are suc-cessfully studied. The results reveal that the natural frequency of circular curved nanobeam is significantly in-fluenced by these effects.

Wave propagation of coupled double-DWBNNTs conveying fluid-systems using different nonlocal surface piezoelasticity theories

ABSTRACTThis work is concerned with the size-dependent wave propagation of coupled double-walled boron nitride nanotubes (DWBNNTs) conveying nanoflow-systems based on Timoshenko beam theory. The two DWBNNTs are coupled by an enclosing visco-Pasternak medium. The small-scale effects are captured applying different surface piezoelasticity theories, including stress gradient, strain gradient, and strain inertia gradient. An analytical method is proposed to obtain phase velocity, cut-off, and escape frequencies of the system. Three cases of in-phase wave propagation, out-of-phase wave propagation, and wave propagation with one DWBNNT fixed are considered. Results indicate that ignoring surface and small-scale effects lead to inaccurate results.

On 3d bulk geometry of Virasoro coadjoint orbits: orbit invariant charges and Virasoro hair on locally AdS $$_3$$ 3 geometries

Expanding upon [arXiv:1404.4472, 1511.06079], we provide further detailed analysis of Ba\~nados geometries, the most general solutions to the AdS3 Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon and boundary structure, and geodesic motion on these geometries, as well as the two class of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate further the one-to-one relation between the coadjoint orbits of two copies of Virasoro group and Ba\~nados geometries. We discuss that the information about the Ba\~nados goemetries fall into two categories: "orbit invariant" information and "Virasoro hairs". The former are geometric quantities while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have some number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS3 Einstein gravity.

Graph properties for nonlocal minimal surfaces

In this paper we show that a nonlocal minimal surface which is a graph outside a cylinder is in fact a graph in the whole of the space. As a consequence, in dimension 3, we show that the graph is smooth. The proofs rely on convolution techniques and appropriate integral estimates which show the pointwise validity of an Euler–Lagrange equation related to the nonlocal mean curvature.

Thermo-electro-mechanical vibration analysis of size-dependent nanobeam resting on elastic medium under axial preload in presence of surface effect

In the present manuscript, a nonclassical beam theory is developed to analyze free vibration of piezoelectric nanobeam by considering surface effects resting on Winkler–Pasternak elastic medium and thermal loading with axial preload. The nonclassical Eringen theory is utilized to incorporate the length-scale parameter to account for the small-scale effect, while the Gurtin–Murdoch model is employed to inject the surface effects including surface elasticity, surface stress and surface density. The governing equations are derived using Hamilton’s principle in the framework of Euler–Bernoulli beam theory. The governing partial differential equations of motions of system are reduced to a set of algebraic equations with the help of differential transformation method as a semi-analytical–numerical. The mathematical derivations and numerical results are presented in detail for various boundary conditions. Some numerical examples are illustrated in order to investigate the effect of several parameters such as the nonlocal parameter, piezoelectric voltage, surface effects, temperature change, axial preload and elastic medium parameters. Moreover, it is also indicated that the numerical results have good agreement with previous studies.

A Semi-Analytical Evaluation of Surface and Nonlocal Effects on Buckling and Vibrational Characteristics of Nanotubes with Various Boundary Conditions

In the present paper, the vibrational and buckling characteristics of nanotubes with various boundary conditions are investigated considering the coupled effects of nonlocal elasticity and surface effects, including surface elasticity and surface tension. The nonlocal Eringen theory is adopted to consider the effect of small scale size, and the Gurtin–Murdoch model the surface effect. Hamilton’s principle is employed to formulate the governing equation and differential transformation method (DTM) is utilized to obtain the natural frequency and critical buckling load of nanotubes with various boundary conditions. The results obtained match the available ones in the literature. Detailed mathematical derivations are presented and numerical investigations are performed. The emphasis is placed on the effects of several parameters, such as the nonlocal parameter, surface effect, aspect ratio, mode number and beam size, on the normalized natural frequencies and critical buckling loads of the nanotube. It is explicitly shown that the vibration and buckling of a nanotube is significantly influenced by these effects. Numerical results are presented which may serve as benchmarks for future analysis of nanotubes.

The effect of sample particle size on the determination of pore structure parameters in shales

The combination of low-pressure N2 and CO2 adsorption could provide an effective approach for characterizing the pore structure of shales. Although gas adsorption methods generally do not destroy the pore structure during experimental process, sample particle sizes could significantly affect experimental results that can approach or deviate from the real value. Therefore, the determination of pore structure is closely related to the sample particle size. In the current study, 4 fresh core samples of different compositions and total organic carbon (TOC) ranges collected from the Sichuan Basin were analyzed to elucidate the effect of sample particle size on the determination of pore structure parameters. Samples were ground and then sieved into seven groups based on particle size ranges, i.e., <60, 60–80, 80–100, 100–120, 120–140, 140–200 and >200 mesh, for measurements of low-pressure N2 and CO2 adsorption, TOC contents, and X-ray diffraction (XRD) mineralogy.TOC results show a slight enrichment whereas XRD minerals vary irregularly, with sample particle size decreases. Meanwhile, the TOC and mineral contents show insignificant statistical relation with pore structure parameters in all sample particle size ranges. Therefore, variations in organic matter content and mineral composition that result from sieving are unlikely to have a significant influence on the pore structure of shale. Rather, sample particle size may be the most important control on pore structure characteristics in the samples analyzed in this study.The relative standard deviations (RSDs) for Brunauer–Emmett–Teller (BET) N2 surface areas, Dubinin–Radushkevich (D–R) CO2 micropore surface areas and non-local density functional theory (NLDFT) N2 and CO2 nanopore surface areas measurements are <5%, within analytical error. Therefore, in the studied grain size range (60–200 mesh), the sample particle size shows insignificant effects on surface area results. However, samples with smaller particle size have a greater effect on pore volume and pore size, especially for pore size distribution (PSD) of N2 low-pressure adsorption. The RSDs of the Barrett–Joyner–Halenda (BJH) pore volumes and BET pore sizes of all samples in the 140–200 mesh range are obviously greater than the values of other mesh ranges. Moreover, in the dV/dlogw plots of PSD analysis, high N2 peaks and new N2 peaks appeared in the 10–100nm pore-width range, particularly for samples in the >140 mesh range. The 60–140 mesh particle-size range is therefore recommended for N2 low-pressure adsorption. Finally, the sample particle size has insignificant effect on the pore system parameters for grains in the 60–200 mesh range for CO2 low-pressure adsorption. Overall, the results confirm that the 60–140 mesh particle-size range can be used for both N2 and CO2 low-pressure adsorption measurements.

Nonlinear vibration and adhesion instability of Casimir-induced nonlocal nanowires with the consideration of surface energy

The following research work deals with the size-dependent dynamic instability of suspended nanowires in the presence of Casimir force and surface effects. Specifically, the Casimir-induced instability of nanostructures with circular cross-section and cylinder-plate geometry is studied. Following the Gurtin–Murdoch model and nonlocal elasticity, the governing equation of motion for nanowires is derived. To express the Casimir attraction of cylinder-plate geometry, two approaches, e.g. proximity force approximation (PFA) for small separations and Dirichlet asymptotic approximation for large separations are studied. To overcome the difficulties for solving a nonlinear problem, a step-by-step numerical method is utilized. The effects of nonlocal parameter, surface energy and vacuum fluctuations on the dynamic instability characteristic and adhesion time of nanowires are studied. It is observed that the phase portrait of Casimir-induced nanowires exhibit periodic and homoclinic orbits.

A Novel Beam-Elastic Substrate Model with Inclusion of Nonlocal Elasticity and Surface Energy Effects

A force-based beam-elastic substrate model incorporating nonlocal elasticity and surface energy effects is developed. The nonlocal elasticity theory is used to capture the nanosized-dependent effect of the beam bulk material while Gurtin–Murdoch surface theory is used to account for the surface energy-dependent size effect. Interaction mechanism between the beam and the surrounding substrate medium is represented by the Winkler-like model. Similarity between the current system and the beam-Winkler–Pasternak foundation system is observed. Consequently, the beam-Winkler–Pasternak foundation element previously proposed by the first two authors can be employed to perform three numerical simulations to investigate the characteristics and behaviors of a beam-substrate system with inclusion of nonlocal elasticity and surface effects.

Magnetic circular dichroism of non-local surface lattice resonances in magnetic nanoparticle arrays.

Subwavelength metallic particles support plasmon resonances that allow extreme confinement of light down to the nanoscale. Irradiation with left- and right hand circularly polarized light results in the excitation of circular plasmon modes with opposite helicity. The Lorenz force lifts the degeneracy of the two modes in magnetic nanoparticles. Consequently, the confinement and frequency of localized surface plasmon resonances can be tuned by an external magnetic field. In this paper, we experimentally demonstrate this effect for nickel nanoparticles using magnetic circular dichroism (MCD). Besides, we show that non-local surface lattice resonances in periodic arrays of the same nanoparticles significantly enhance the MCD signal. A numerical model based on the modified long wavelength approximation is used to reproduce the main features in the experimental spectra and provide design rules for large MCD effects in sensing applications.

Nonlocal fluid mechanics description of solvation forces

In this paper an analytical expression for the solvation force, based on the nonlocal surface stress due to the nonlocal density variation, is constructed by making a surface functional approximation to the general stress constitutive equation of nonlocal viscous fluids. It is then applied to derive a well-known semi-empirical expression for solvation forces.

Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams

To investigate the surface effects on thermomechanical vibration and buckling of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension, and surface density for modeling the nanoscale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported nanobeam at both ends. Solving these equations enables us to estimate the natural frequency and critical buckling load for circular curved nanobeam including Winkler and Pasternak elastic foundations and under the effect of a uniform temperature change. The results determined are verified by comparing the results with available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations, temperature, and opening angle of circular curved nanobeam on the natural frequency and critical buckling load are successfully studied. The results reveal that the natural frequency and critical buckling load of circular curved nanobeam are significantly influenced by these effects.

Free dynamic analysis of functionally graded tapered nanorods via a newly developed nonlocal surface energy-based integro-differential model

The nonlocality effect based on appropriate kernel functions plays an important role in mechanical analysis of nanostructures. This phenomenon is not limited to the bulk, but also includes the surface layer. However, these important issues have not been properly paid attention to in the previously developed continuum-based models. Using a novel nonlocal integro-differential model accounting for the surface energy effect, free longitudinal vibration of functionally graded tapered nanorods embedded in an elastic matrix is investigated. The material properties of both the bulk and the surface layer vary along the nanorod’s length based on a power-law relation. By considering the nonlocal integro-differential constitutive relations for the bulk as well as the surface layer, the equations of motion of the elastically supported nanostructure are obtained and analyzed via reproducing kernel particle method (RKPM). In particular cases, modal analysis is also implemented and the obtained results by the RKPM are successfully verified with those of the modal analysis approach. The roles of the surface energy, small-scale parameter, stiffness of the matrix and that of the supports, nanorod’s diameter, power-law index, and the nonlocal kernel function on the natural frequencies are explained in some detail.

Scale Effect on Flexural Wave Propagation in Embedded Single-Walled Carbon Nanotubes: Nonlocal Small-Size Effect and Surface Effect

Scale Effect on Flexural Wave Propagation in Embedded Single-Walled Carbon Nanotubes: Nonlocal Small-Size Effect and Surface Effect

A triple-resonance Raman chip for simultaneous enhancement of Stokes and anti-Stokes lines utilizing both localized and non-localized plasmonic resonance

In this paper we report a triple-resonance surface-enhanced Raman scattering (SERS) chip that is able to provide simultaneous field enhancement for both the Stokes and anti-Stokes lines. The structure consists of an array of periodic gold bowties placed on the surface of a uniform gold film. It can support two localized surface plasmonic resonances (LSPRs): an electric dipole binding resonance (EDBR) and a magnetic dipole resonance (MDR). A third field enhancement peak is obtained by utilizing the strong interaction between the non-localized surface plasmonic resonance (non-localized SPR) and the LSPR, which greatly raises the field enhancement for the non-localized SPR. In addition, a gold strip-line resonator is incorporated to further enhance the local field intensity. Consequently, the field enhancement of the three peaks are all increased. Compared with the same structure without strip, the periodic bowtie-strip compound structure on gold film can gain as much as ∼22.8 times and ∼3.6 times larger Raman intensity enhancement simultaneously for both the Stokes and anti-Stokes lines.

Robust local and nonlocal transport in the topological Kondo insulatorSmB6in the presence of a high magnetic field

${\mathrm{SmB}}_{6}$ has been predicted to be a Kondo topological insulator with topologically protected conducting surface states. We have studied quantitatively the electrical transport through surface states in high-quality single crystals of ${\mathrm{SmB}}_{6}$. We observe a large nonlocal surface signal at temperatures lower than the bulk Kondo gap scale. Measurements and finite-element simulations allow us to distinguish unambiguously between the contributions from different transport channels. In contrast to general expectations, the electrical transport properties of the surface channels were found to be insensitive to high magnetic fields. We propose possible scenarios that might explain this unexpected finding. Local and nonlocal magnetoresistance measurements allowed us to identify possible signatures of helical spin states and strong interband scattering at the surface.

Surface and non-local effects for non-linear analysis of Timoshenko beams

In this paper, we present a non-local non-linear finite element formulation for the Timoshenko beam theory. The proposed formulation also takes into consideration the surface stress effects. Eringen׳s non-local differential model has been used to rewrite the non-local stress resultants in terms of non-local displacements. Geometric non-linearities are taken into account by using the Green–Lagrange strain tensor. A C0 beam element with three degrees of freedom has been developed. Numerical solutions are obtained by performing a non-linear analysis for bending and free vibration cases. Simply supported and clamped boundary conditions have been considered in the numerical examples. A parametric study has been performed to understand the effect of non-local parameter and surface stresses on deflection and vibration characteristics of the beam. The solutions are compared with the analytical solutions available in the literature. It has been shown that non-local effect does not exist in the nano-cantilever beam (Euler–Bernoulli beam) subjected to concentrated load at the end. However, there is a significant effect of non-local parameter on deflections for other load cases such as uniformly distributed load and sinusoidally distributed load (Cheng et al. (2015) [10]). In this work it has been shown that for a cantilever beam with concentrated load at free end, there is definitely a dependency on non-local parameter when Timoshenko beam theory is used. Also the effect of local and non-local boundary conditions has been demonstrated in this example. The example has also been worked out for other loading cases such as uniformly distributed force and sinusoidally varying force. The effect of the local or non-local boundary conditions on the end deflection in all these cases has also been brought out.

Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory

Control and analyze the nonlinear dynamic stability of single layered graphene sheets (SLGSs) integrated with zinc oxide (ZnO) actuators and sensors are the main contributions of present work. In order to present a realistic model, the material properties of system are assumed viscoelastic using Kelvin–Voigt model. The surrounding elastic medium is simulated with nonlinear orthotropic visco-Pasternak foundation. Considering refined zigzag theory (RZT), a new formulation is developed through the Gurtin–Murdoch elasticity theory in which the effects of surface stress are incorporated. A novel numerical procedure namely as differential cubature (DC) method is applied for solution. A proportional-derivative (PD) controller is used for the active control of the system dynamic stability. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, viscoelastic foundation, surface stress, applied voltage, controller and structural damping on the dynamic instability region (DIR) of system. The accuracy of the proposed method is verified by comparing its numerical prediction with other published works as well as solution of system with differential quadrature (DQ) and harmonic differential quadrature (HDQ) methods. Results depict that the magnetic field and external voltage are effective controlling parameters for DIR of system.

Postbuckling of Unknown-Length Nanobeam Considering the Effects of Nonlocal Elasticity and Surface Stress

The objective of this paper is to study the postbuckling behaviors of an unknown-length nanobeam combined with small-scale effects. The concept of variable-arc-length elastica is firstly applied on the problem of nanobeams. The span length is not changed while the arc length is varied increasingly. The nanobeam is on a clamped support at one end, while the other end is an overhanging part through a frictionless slot subjected to axial compression. At this end, the nanobeam is movable only in a horizontal direction. The governing equation is developed by the moment–curvature relationship based on the classical Euler–Bernoulli beam theory, including the effects of nonlocal elasticity, residual surface stress, and both combined effects. The shooting–optimization technique with two-point boundary condition is employed to solve the differential equations in this problem. The results, including nonlocal elasticity, reveal that nanobeams have decreased structural stiffness; meanwhile, the residual surface tension and both combined effects have increased strength. The postbuckling loads decrease as the arc length of nanobeams is increased. The equilibrium configurations are close to an anti-loop for very large deflections. The friction force at the nanoslot is also considered.

Thermal effect on terahertz wave propagations in nanotube conveying fluid

An accurate model about the terahertz wave propagation in fluid-filled single-walled carbon nanotube, named non-local Euler–Bernoulli bean models, was studied in the past decade. The temperature is a key factor to study the mechanical properties of the nanostructures. This paper presents the thermal effect about single-walled carbon nanotubes. The governing equation for single-walled carbon nanotubes is developed through non-local Timoshenko beam theory, and size and surface effects are considered. The fluid flows quickly, and the terahertz wave propagation will be in the scope of the frequency. Thermal effect and liquid density significantly change the propagating frequency.