An analytical symplectic approach to the vibration analysis of orthotropic graphene sheets

A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach. A Hamiltonian system is established by introducing a total unknown vector consisting of the displacement amplitude, rotation angle, shear force, and bending moment. The high-order governing differential equation of the vibration of SLGSs is transformed into a set of ordinary differential equations in symplectic space. Exact solutions for free vibration are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary conditions. Vibration modes are expressed in terms of the symplectic eigenfunctions. In the numerical examples, comparison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given. A parametric study of the natural frequency is also included.

Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media

An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D)viscoelastic media.The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials.Within the framework of symplectic elasticity,the governing equations in the Hamiltonian form for the frequency domain(s-domain)can be directly and rigorously calculated.In the s-domain,the analytical solutions of the displacement and stress fields are constructed by superposing the symplectic eigensolutions without any trial function,and the explicit expressions of the intensity factors and J-integral are derived simultaneously.Comparison studies are provided to validate the accuracy and effectiveness of the present solutions.A detailed analysis is made to reveal the effects of viscoelastic parameters and applied loads on the intensity factors and J-integral.

MICROCRYSTALLINE STRUCTURE STUDY DEMINERALIZATION AND REMINERALIZATION OF THE ARTIFICIAL CARIES OF HUMAN TOOTH ENAMEL

Microcrystalline structure changes of teeth enamel crystals during the artificial caries and synthetic saliva reminerlization were reported. Enamel samples were thinned by argon-ion-milling and examined by high-resolution transmitting electron microscope. The results revealed that the lattice dissolution of enamel hydroxyapatite started from central parts and grain boundaries of crystals, the former were often parallel to (1010) plane and advancing along the [0001] zone axis of crystals. The results also shown that synthetic saliva may reduce the quantity of bright contrast spots in lattice image for artificial carious crystals. In addition, some defects such as dislocations were found in grains, and they are believed to be related to the dissolution of lattice. Three kinds of structural weak sites revealed in crystals, i. e. (1)dislocations, (2) vacancies or impurities, and (3) grain boundaries.

Layer Structure of Doped C_(60)

It is found in this letter that the doped C_(60) possesses layer-structure in both bond distortions and electronic states.There are eight layers of carbon atoms in the charged C_(60),and its symmetry is reduced from Ih to D_(5d).This layer-structure indicates that there exist four nonequivalent groups of carbon atoms in the doped C_(60).It contrasts with the pristine C_(60),in which all the sixty carbon atoms are equivalent.One observable consequence of such layer-structure is the split of its NMR spectrum with the ratio 1:1:2:2.

Design optimization of the S-frame to improve crashworthiness

In this paper, the S-frames, the front side rail structures of automobile, were investigated for crashworthihess. Various cross-sections including regular polygon, nonconvex polygon and multi-cell with inner stiffener sections were investigated in terms of energy absorption of S-frames. It was determined through extensive numerical simulation that a multi-celI S-frame with double vertical internal stiffeners can absorb more energy than the other configurations. Shape optimization was also carried out to improve energy absorption of the S-frame with a rectangular section. The center composite design of experiment and the sequential response surface method （SRSM） were adopted to construct the approximate design sub-problem, which was then solved by the feasible direction method. An innovative double S- frame was obtained from the optimal result. The optimum configuration of the S-frame was crushed numerically and more plastic hinges as well as shear zones were observed during the crush process. The energy absorption efficiency of the structure with the optimal configuration was improved compared to the initial configuration.

Application of Hamiltonian system for two-dimensional transversely isotropic piezoelectric media

This paper presents a symplectic method for two-dimensional transversely isotropic piezoelectric media with the aid of Hamiltonian system. A symplectic system is established directly by introducing dual variables and a complete space of eigensolutions is obtained. The solutions of the problem can be expressed by eigensolutions. Some solutions, which are local and are neglected usually by Saint Venant principle, are shown. Curves of non-zero-eigenvalues and their eigensolutions are given by the numerical results.

FAST SOLUTION FOR LARGE SCALE LINEAR ALGEBRAIC EQUATIONS IN FINITE ELEMENT ANALYSIS

The computational efficiency of numerical solution of linearalgebraic equations in finite elements can be improved in two ways.One is to decrease the fill-in numbers, which are new non-ze- ronumbers in the matrix of global stiffness generated during theprocess of elimination. The other is to reduce the computationaloperation of multiplying a real number by zero. Based on the factthat the order of elimination can determine how many fill-in numbersshould be generated, we present a new method for optimization ofnumbering nodes. This method is quite different from bandwidthoptimiza- tion. Fill-in numbers can be decreased in a large scale bythe use of this method. The bi-factorization method is adopted toavoid multiplying real numbers by zero. For large scale finiteelement analysis, the method presented in this paper is moreefficient than the traditional LDLT method.

Oxidation Experiment of Natural Megacrystal Clinopyroxene:Implications for Assignment of Mssbauer Spectra

The M?ssbauer spectra of natural megacrystal clinopyroxene are usually fitted by 4 sets of symmetric doublets, A-A', B-B', C-C' and D-D', respectively, in terms of increasing Qs value in literature. But the assignments of those doublets are quite different, except the D-D' doublet assigned to Fe3+at the lattice site M***1 in previous papers. Particularly, the assignment and interpretation of the C-C' doublet are diverse.

Tensile strength of sea ice using splitting tests based on the digital image correlation method

The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.

Analytical and numerical methods of symplectic system for Stokes flow in two-dimensional rectangular domain

In this paper, a new analytical method of symplectic system, Hamiltonian system, is introduced for solving the problem of the Stokes flow in a two-dimensional rectangular domain. In the system, the fundamental problem is reduced to an eigenvalue and eigensolution problem. The solution and boundary conditions can be expanded by eigensolutions using adjoint relationships of the symplectic ortho-normalization between the eigensolutions. A closed method of the symplectic eigensolution is presented based on completeness of the symplectic eigensolution space. The results show that fundamental flows can be described by zero eigenvalue eigensolutions, and local effects by nonzero eigenvalue eigensolutions. Numerical examples give various flows in a rectangular domain and show effectiveness of the method for solving a variety of problems. Meanwhile, the method can be used in solving other problems.

TORSIONAL PROPERTIES OF METALLIC NANOSPRINGS

Based on molecular mechanics and the embedded-atom potential, the torsional mechanical behaviors of metallic copper nanosprings are investigated in this paper. The torsion coefficient of the nanospring is obtained by fitting the curve of potential energy versus torsion angle according to a parabolic law. It is found that the geometry of nanospring has a strong influence on the torsion coefficient. With the increase of the wire radius and the helix radius, the torsion coefficient of the nanospring increases. However, it decreases with the increase of the helix pitch and turns. It is also found that the classic spring theory is invalid to torsional nanosprings. The calculated torsion coefficient is higher than the predication from the classic spring theory and is lower than that of the corresponding solid rod. In addition, the continuum mechanics is shown to be inapplicable to describe the torsional behavior of nanosprings. These findings might provide a better understanding of the usability and functionality of nanosprings in nanodevices.

A Symplectic Method of Numerical Simulation on Local Buckling for Cylindrical Long Shells under Axial Pulse Loads

In this paper,the local buckling of cylindrical long shells is discussed under axial pulse loads in a Hamiltonian system.Using this system,critical loads and modes of buckling of shells are reduced to symplectic eigenvalues and eigensolutions respectively.By the symplectic method,the solution of the local buckling of shells can be employed to the expansion series of symplectic eigensolutions in this system.As a result,relationships between critical buckling loads and other factors,such as length of pulse load,thickness of shells and circumferential orders,have been achieved.At the same time,symmetric and unsymmetric buckling modes have been discuss.Moreover,numerical results show that modes of post-buckling of shells can be Bamboo node-type,bending type,concave type and so on.Research in this paper provides analytical supports for ultimate load prediction and buckling failure assessment of cylindrical long shells under local axial pulse loads.

Observation of Hot Electrons in Surface-Wave Plasmas Excited by Surface Plasmon Polaritons

The electron energy distribution functions(EEDFs)are studied in the planar-type surface-wave plasma(SWP)caused by resonant excitation of surface plasmon polaritons(SPPs)using a single cylindrical probe.Sustained plasma characteristics can be considered as a bi-Maxwellian EEDF,which correspond to a superposition of the bulk low-temperature electron and the high-energy electron beam-like part.The beam component energy is pronounced at about 10 eV but the bulk part is lower than 3.5 eV.The hot electrons included in the proposed plasmas play a significant role in plasma heating and further affect the discharge chemistry.

Finding Discontinuous Solutions to the Differential-Difference Equations by the Homotopy Analysis Method

An analytic method,namely the homotopy analysis method,is applied to nonlinear problems with discontinuity governed by the differential-difference equation.Purely analytic solutions are given for nonlinear problems with discontinuity with a global convergence.This method provides a new analytical approach to solve nonlinear problems with discontinuity.Comparisons are made between the results of the proposed method and the exact solutions.The results reveal that the proposed method is very effective and convenient.

Electromagnetic interaction between local surface plasmon polaritons and an atmospheric surface wave plasma jet

We analyze the electromagnetic interaction between local surface plasmon polaritons （SPPs） and an atmospheric surface wave plasma jet （ASWPJ） in combination with our designed discharge device. Before discharge, the excitation of the SPPs and the spatial distribution of the enhanced electric field are analyzed. During discharge, the critical breakdown electric field of the gases at atmospheric gas pressure and the surface wave of the SPPs converted into electron plasma waves at resonant points are studied. After discharge, the ionization development process of the ASWPJ is simulated using a two- dimensional fluid model. Our results suggest that the local enhanced electric field of SPPs is merely the precondition of gas breakdown, and the key mechanism in maintaining the discharge development of a low-power ASWPJ is the wave-mode conversion of the local enhanced electric field at the resonant point.

Character Diagnosis for Surface-Wave Plasmas Excited by Surface Plasmon Polaritons

The plasma parameters of planar-type surface-wave plasmas （SWPs） are diagnosed based on the resonant excitation of surface plasmon polaritons （SPPs）. The plasma parameter distributions are obtained by changing the discharge conditions of gas pressure and incident power. The measured experimental results show that the plasma near the heating layer is excited by surface waves of SPPs while the plasma located downstream originates from diffusion Moreover, the influence of high-frequency oscillations plays a significant role in producing the proposed SWPs with bi-Maxwellian electron energy distributions.

A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media

This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are re- duced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigen- solutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.

浅水短波Degasperis-Procesi方程的环形孤立波解(英文)

An analytic method, i.e. the homotopy analysis method, was applied for constructing the solutions of the short waves model equations associated with the Degasperis-Procesi (DP) shallow water waves equation. The explicit analytic solutions of loop soliton governing the propagation of short waves were obtained. By means of the transformation of independent variables, an analysis one-loop soliton solution expressed by a series of exponential functions was obtained, which agreed well with the exact solution. The results reveal the validity and great potential of the homotopy analysis method in solving complicated solitary water wave problems.

Solving shock wave with discontinuity by enhanced differential transform method(EDTM)

An enhanced differential transform method （EDTM）, which introduces the Pad@ technique into the standard differential transform method （DTM）, is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact Dower series solution.

Editorial:Computational granular mechanics

Granular materials exist widely in nature,industry and engineering applications and perform complex mechanical behaviors.Theoretical analysis,numerical simulations and physical experiments were adopted to investigate the mechanical properties of granular systems and to solve the engineering problems.The discrete element method(DME)was proposed in 1970s and has been a practical approach to study the macro and mesoscopic behaviors of various granular materials.Although numerical methods have been successfully applied to the study of basic physical and mechanical properties of granular materials,there are still many challenges in computational granular mechanics,such as the construction of real particle morphology,flow characteristics of granular materials,multi-media and multiscale modelling and high-performance computational algorithms.