A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

In this pap er, a novel size-dep endent functionally graded (FG) cylindrical shell model is develop ed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory . The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical typ es of size e ects simultaneously , which are the nonlocal stress ef- fect, the strain gradient e ect, and the surface energy e ects. With the help of Hamilton’s principle and rst-order shear deformation theory , the non-classical governing equations and related b oundary conditions are derived. By using the prop osed model, the free vibra- tion problem of FG cylindrical nanoshells with material prop erties varying continuously through the thickness according to a p ower-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various b oundary conditions are obtained. After verifying the reliability of the prop osed model and analytical method by comparing the degenerated results with those available in the literature, the in uences of nonlocal parameter, material length scale parameter, p ower-law index, radius-to-thickness ratio, length-to-radius ratio, and surface e ects on the vibration characteristic of func- tionally graded cylindrical nanoshells are examined in detail.

Large-area straight,regular periodic surface structures produced on fused silica by the interference of two femtosecond laser beams through cylindrical lens

Inhomogeneity and low efficiency are two important factors that limit the application of laser-induced periodic surface structures(LIPSSs),especially on glass surfaces.In this study,two-beam interference(TBI)of femtosecond lasers was used to produce large-area straight LIPSSs on fused silica using cylindrical lenses.Compared with those produced us-ing a single circular or cylindrical lens,the LIPSSs produced by TBI are much straighter and more regular.Depending on the laser fluence and scanning velocity,LIPSSs with grating-like or spaced LIPSSs are produced on the fused silica sur-face.Their structural colors are blue,green,and red,and only green and red,respectively.Grating-like LIPSS patterns oriented in different directions are obtained and exhibit bright and vivid colors,indicating potential applications in surface coloring and anti-counterfeiting logos.

An experimental research on surface oscillation of buoyant-thermocapillary convection in open cylindrical annuli

An experiment is carried out on the surface oscillation of buoyant-thermocapillary convection in an open cylindrical annulus. When the radial temperature difference AT reaches a critical value △Tc, a regular oscillation appears and soon disappears on the open surface, which varies when the liquid layer＇s thickness h and temperature difference △T are varied. With growth of △T, dominant frequency of the visible oscillation will grow too but is found within certain frequencies. Driving forces, buoyance and thermocapillarity, are responsible for this phenomanon and the ＂balance＂ point is considered to exist when h is between 4.5-5.0 mm. Surface oscillation region is also found restricted within a narrow gap when Bo is smaller than 3.7.

Analytical solution approach for nonlinear buckling and postbuckling analysis of cylindrical nanoshells based on surface elasticity theory

The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman＇s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuekling characteristics of nanoshells with small sizes.

Size-dependent surface tension of a cylindrical nanobubble in liquid Ar

In view of the continued disputes on the fundamental question of whether the surface tension of a vapour bubble in liquid argon increases, or decreases, or remains unchanged with the increase of curvature radius, a cylindrical vapour bubble of argon is studied by molecular dynamics simulation in this paper instead of spherical vapour bubble so as to reduce the statistical error. So far, the surface tension of the cylindrical vapour bubble has not been studied by molecular dynamics simulation in the literature. Our results show that the surface tension decreases with radius increasing. By fitting the Tolman equation with our data, the Tolman length σ = -0.6225 sigma is given under cut-off radius 2.5σ, where σ = 0.3405 nm is the diameter of an argon atom. The Tolman length of Ar being negative is affirmed and the Tolman length of Ar being approximately zero given in the literature is negated, and it is pointed out that this error is attributed to the application of the inapplicable empirical equation of state and the neglect of the difference between surface tension and an equimolar surface.

A Self-Consistent Model on Cylindrical Monopole Plasma Antenna Excited by Surface Wave Based on the Maxwell-Boltzmann Equation

The paper analyzes the motion of electron in plasma antenna and the distribution of electromagnetic field power around the plasma antenna, and proposes a self-consistent model according to the structure of cylindrical monopole plasma antenna excited by surface wave;calculation of the model is based on Maxwell-Boltzmann equation and gas molecular dynamics theory. The calculation results show that this method can reflect the relationships between the external excitation power, gas pressure, discharge current and the characteristic of plasma. It is an accurate method to predicate and calculate the parameters of plasma antenna.

Influence of Spray Gun Position and Orientation on Liquid Film Development along a Cylindrical Surface

A method combining computationalfluid dynamics(CFD)and an analytical approach is proposed to develop a prediction model for the variable thickness of the spray-induced liquidfilm along the surface of a cylindrical workpiece.The numerical method relies on an Eulerian-Eulerian technique.Different cylinder diameters and positions and inclinations of the spray gun are considered and useful correlations for the thickness of the liquidfilm and its distribution are determined using various datafitting algorithms.Finally,the reliability of the pro-posed method is verified by means of experimental tests where the robot posture is changed.The provided cor-relation are intended to support the optimization of spray-based coating applications.

Numerical Simulation Study on the Surface Deflection of Cylindrical Shallow Shell

The increasing applications of new materials such as high strength low alloy (HSAL) steels and aluminum alloy sheets have lead to greater focus on the surface deflections of auto body panels in the automobile industry in recent years.The finite element models of cylindrical shallow shell that can represent auto body panels are established.Numerical simulations of forming and unloading of cylindrical shallow shell are carried out.And a measurement and evaluation method of the surface deflection is introduced.The simulations of surface deflections with various blank homing forces (BHF) show great agreement with the experi- mental results.The influence laws of sheet thickness and material properties such as yield strengthσs,strain-hardening exponent n,anisotropy parameter r and strength coefficient k on the surface deflection are achieved by simulations,which give a basic refer- ence for controlling surface deflections.

NONLINEAR STABILITY ANALYSIS OF A SANDWICH SHALLOW CYLINDRICAL PANEL WITH ORTHOTROPIC SURFACES

In this paper, the large deflection theory is adopted to analyse the geometrical nonlinear stability of a sandwich shallow cylindrical panel with orthoiropic surfaces. The critical point is determined and the postbitckling behaviour of the panel is studied.

Dynamic behavior of single-layer latticed cylindrical shells subjected to seismic loading

The single-layer latticed cylindrical shell is one of the most widely adopted space-fl'amed structures.In this paper,free vibration properties and dynamic response to horizontal and vertical seismic waves of single-layer latticed cylindrical shells are analyzed by the finite element method using ANSYS software.In the numerical study,where hundreds of cases were analyzed,the parameters considered included rise-span ratio,length-span ratio,surface load and member section size.Moreover,to better define the actual behavior of single-layer latticed shells,the study is focused on the dynamic stress response to both axial forces and bending moments.Based on the numerical results,the effects of the parameters considered on the stresses are discussed and a modified seismic force coefficient method is suggested.In addition,some advice based on these research results is presented to help in the future design of such structures.

Model experiment of rock blasting with single borehole and double free-surface

In order to improve the quality of laneways and tunnel excavation by drilling and blasting and by making effective use of explosive energy, a model experiment of rock blasting with a single borehole and a double free-surface was performed with the objective of studying the effect of parameters such as charge structure, free-surface and rock compressive strength on rock blasting.The model experiments indicate that:1) the smaller the rock compressive strength and density, the more distinctive the cavity expanding action by blasting;2) the powder factor in an air-decoupling charge structure is larger than that in a coupling charge structure, i.e., the explosive energy in an air-decoupling charge structure transferred to the rocks is less than that in a coupling charge structure;3) a free-surface improves the utilizations of explosive energy;4) an air-decoupling charge structure helps to maintain the integrity and stability of wall rock in controlled perimeter blasting, such as in roadways and tunnel excavation by drilling and blasting.

Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires： transfer matrix method

The polar interface optical （IO） and surface optical （SO） phonon modes and the corresponding Froehlich electron phonon-interaction Hamiltonian in a freestanding multi-layer wurtzite cylindrical quantum wire （QWR） are derived and studied by employing the transfer matrix method in the dielectric continuum approximation and Loudon＇s uniaxial crystal model. A numerical calculation of a freestanding wurtzite GaN/AlN QWR is performed. The results reveal that for a relatively large azimuthal quantum number m or wave-number kz in the free z-direction, there exist two branches of IO phonon modes localized at the interface, and only one branch of SO mode localized at the surface in the system. The degenerating behaviours of the IO and SO phonon modes in the wurtzite QWR have also been clearly observed for a small kz or m. The limiting frequency properties of the IO and SO modes for large kz and m have been explained reasonably from the mathematical and physical viewpoints. The calculations of electron-phonon coupling functions show that the high-frequency IO phonon branch and SO mode play a more important role in the electron phonon interaction.

Analytic wave series solution of out-of-plane(SH) waves diffraction by an almost semi-circular shallow cylindrical hill

A closed-form wave equation analytic solution of two-dimensional scattering and diffraction of outof-plane（SH） waves by an almost semi-circular shallow cylindrical hill on a flat, elastic and homogeneous half space is proposed by applying the discrete Fourier series expansions of sine and cosine functions. The semi-circular hill problem is discussed as a special case for the new formulated equation.Compared with the previous semi-circular cases solutions, the present method can give surface displacement amplitudes which agrees well with previous results. Although the proposed equation can only solve the problem of SH-waves diffracted by almost semi-circular shallow hills, the stress and displacement residual amplitudes are numerical insignificantly everywhere. Moreover, the influences of the depth-towidth ratio（a parameter defined in this paper to evaluate the shallowness of the topography of hills） on ground motions are presented and summarized. The limitations and errors of truncation from Graf’s addition theorem and Fourier series equations in the present paper are also discussed.

Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length: Functional Theoretical Approach

With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities cointide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeψ〈〈kT is introduced.

On the Ruled surfaces in Minkowski 3-space R1^3

Izumiya and Takeuchi （2003） obtained some characterizations for Ruled surfaces. Turgut and Haclsalihoglu （1998） defined timelike Ruled surfaces and obtained some characterizations in timelike Ruled surfaces. Choi （1995） and Jung and Pak （1996） studied Ruled surfaces. This study uses the method in （lzumiya and Takeuchi, 2003） to investigate cylindrical helices and Bertrand curves as curves on timelike Ruled surfaces in Minkowski 3-space R1^3. We have studied singularities of the rectifying developable （surface） of a timelike curve. We observed that the rectifying developable along a timelike curve a is non-singular if and only if a is a cylindrical helice. In this case the rectifying developable is a cylindrical surface.

Vibration Analysis of an Infinite Poroelastic Circular Cylindrical Shell Immersed in Fluid

The purpose of this paper is to study the effect of presence of fluid within and around a poroelastic circular cylindrical shell of infinite extent on axially symmetric vibrations. The frequency equation each for a pervious and an impervious surface is obtained employing Biot’s theory. Radial vibrations and axially symmetric shear vibrations are uncoupled when the wavenumber is vanished. The propagation of axially symmetric shear vibrations is independent of presence of fluid within and around the poroelastic cylindrical shell while the radial vibrations are affected by the presence of fluid. The frequencies of radial vibrations and axially symmetric shear vibrations are the cut-off frequencies for the coupled motion of axially symmetric vibrations. The non-dimensional phase velocity as a function of ratio of thickness to wavelength is computed and presented graphically for two different types of poroelastic materials for thin poroelastic shell, thick poroelastic shell and poroelastic solid cylinder.

Mathematical Model Development and 3D Printing of Cylindrically Shaped Biofilm Carrier Media from Recycled Plastic Waste for Wastewater Treatment

Wastewater management and purification remain one of the greatest problems of mankind. The biological wastewater treatment technique uses a biofilm media carrier where microorganisms attach themselves to the surface. This biofilter is usually made from virgin plastic pellets and can also be produced from recycled waste plastic and used in wastewater treatment. The need to treat water using low-cost carrier media has led to finding alternative sources of materials for biofilter manufacturing. Therefore, this work is centered on the recycling of waste plastic to make filaments which are then used for 3D printing of a high specific surface area (SSA) less clogging biofilm carrier through the parametric redesign. In the current study, the polypropylene material was recycled to make a 2.85 mm diameter filament compatible with the Ultimaker S3. Moreover, analytical models and governing equations were developed for the design of the K3 Kaldnes and MB3 media. Empirical surface area (SA), specific surface area, and volume of the respective carriers were determined using the model developed. SolidWorks was used to design and evaluate the same parameters which were then compared to model results. The errors in SSA obtained from the model with respect to the SolidWorks results for both the K3 Kaldnes and MB3 media were 0.34% and 0.76% respectively. With these small error margins, the model can serve as a tool and guideline for the designing of cylindrically shaped carriers. By transforming plastics into biofilters, waste plastics are mopped up reducing pollutions. Consequently, the deployment of such biofilters will enhance efficient wastewater treatment for a cleaner environment and the wellbeing of human race.

The Ellipsoidal Surface Method Solving by Integration for Slope Stability Analysis

Landslide is common phenomena in construction field. Nowadays the cylindrical surface method has been used widely to analyze slope stability. However, this method contains two main disadvantages： firstly, the slip surface is assumed to be in circular shape while in fact it is ellipsoid commonly; and secondly, resolve by difference method causing immensely complicated process due to statically indeterminate equations. In this paper, the authors have presented a method that allows transferring of ellipsoid slip surface to cylindrical shape and carries out a single variable equation （by applying integration method）. Also thanks to this method, the current cylindrical surface method has been proved that its application is proper for man-made slopes but usually inappropriate for natural ones. Those results help analysis of slope stability reaching closer to reality.

A Predictive Modeling Based on Regression and Artificial Neural Network Analysis of Laser Transformation Hardening for Cylindrical Steel Workpieces

Laser surface hardening is a very promising hardening process for ferrous alloys where transformations occur during cooling after laser heating in the solid state. The characteristics of the hardened surface depend on the physicochemical properties of the material as well as the heating system parameters. To exploit the benefits presented by the laser hardening process, it is necessary to develop an integrated strategy to control the process parameters in order to produce desired hardened surface attributes without being forced to use the traditional and fastidious trial and error procedures. This study presents a comprehensive modelling approach for predicting the hardened surface physical and geometrical attributes. The laser surface transformation hardening of cylindrical AISI 4340 steel workpieces is modeled using the conventional regression equation method as well as artificial neural network method. The process parameters included in the study are laser power, beam scanning speed, and the workpiece rotational speed. The upper and the lower limits for each parameter are chosen considering the start of the transformation hardening and the maximum hardened zone without surface melting. The resulting models are able to predict the depths representing the maximum hardness zone, the hardness drop zone, and the overheated zone without martensite transformation. Because of its ability to model highly nonlinear problems, the ANN based model presents the best modelling results and can predict the hardness profile with good accuracy.

High-precision simulation and experimental verification of residual stress and surface topography of cylindrical surface shot peening

Shot peening is commonly employed for surface deformation strengthening of cylindrical surface part.Therefore,it is critical to understand the effects of shot peening on residual stress and surface topography.Compared to flat surface,cylindrical surface shot peening has two significant features:(i)the curvature of the cylindrical surface and the scattering of the shot stream cause dis-tributed impact velocities;(i)the rotation of the part results in a periodic variation of the impact velocity component.Therefore,it is a challenge to quickly and accurately predict the shot peening residual stress and surface topography of cylindrical surface.This paper developed a high-precision model which considers the more realistic shot peening process.Firstly,a kinematic analysis model was developed to simulate the relative movement of numerous shots and cylindrical surface.Then,the spatial distribution and time-varying impact information was calculated.Subsequently,the impact information was used for finite element modeling to predict residual stress and surface topography.The proposed kinematic analysis method was validated by comparison with the dis-crete element method.Meanwhile,9310 high strength steel rollers shot peening test verified the effectiveness of the model in predicting the residual stress and surface topography.In addition,the effects of air pressure and attack angle on the residual stress and surface topography were investigated.This work could provide a functional package for efficient prediction of the surface integrity and guide industrial application in cylindrical surface shot peening.