Showing papers in "Applied Mathematics and Mechanics-english Edition in 2018"

Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory

Abstract: By means of a comprehensive theory of elasticity, namely, a nonlocal strain gradient continuum theory, size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material (FGM) are examined. To take small scale effects into consideration in a more accurate way, a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory. The variation of material properties associated with FGM nanoshells is supposed along the shell thickness, and it is modeled based on the Mori-Tanaka homogenization scheme. With a boundary layer theory of shell buckling and a perturbation-based solving process, the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly. It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime, while the nonlocal size dependency leads to the decreases of them. Moreover, the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one.

Thermomagnetic effect with microtemperature in a semiconducting photothermal excitation medium

Abstract: The main goal of this paper is to focus on the investigation of interaction between a magnetic field and elastic materials with microstructure, whose microelements possess microtemperatures with photothermal excitation. The elastic-photothermal problem in one-dimension is solved by introducing photothermal excitation at the free surface of a semi-infinite semiconducting medium (semiconductor rod). The integral transform technique is used to solve the governing equations of the problem under the effect of the microtemperature field. The analytical expressions for some physical quantities in the physical domain are obtained with the heating boundary surface and free traction. The numerical inversion technique is used to obtain the resulting quantities in the physical domain. The obtained numerical results with some comparisons are discussed and shown graphically.

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

Abstract: The free thermal vibration of functionally graded material (FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise (UTR), nonlinear temperature rise (NLTR), and linear temperature rise (LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the strain-displacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover, the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

Mesoscale modeling of microgel mechanics and kinetics through the swelling transition

Abstract: The mechanics and swelling kinetics of polymeric microgels are simulated using a mesoscale computational model based on dissipative particle dynamics. Microgels are represented by a random elastic network submerged in an explicit viscous solvent. The model is used to probe the effect of different solvent conditions on the bulk modulus of the microgels. Comparison of the simulation results through the volume phase transition reveals favorable agreement with Flory-Rehner’s theory for polymeric gels. The model is also used to examine the microgel swelling kinetics, and is found to be in good agreement with Tanaka’s theory for spherical gels. The simulations show that, during the swelling process, the microgel maintains a nearly homogeneous structure, whereas deswelling is characterized by the formation of chain bundles and network coarsening.

Chemically reactive and radiative von Kármán swirling flow due to a rotating disk

Abstract: A new mathematical model is presented to study the heat and mass transfer characteristics of magnetohydrodynamic (MHD) Maxwell fluid flow over a convectively heated stretchable rotating disk. To regulate the fluid temperature at the surface, a simple isothermal model of homogeneous-heterogeneous reactions is employed. The impact of nonlinear thermal radiative heat flux on thermal transport features is studied. The transformed nonlinear system of ordinary differential equations is solved numerically with an efficient method, namely, the Runge-Kutta-Felberg fourth-order and fifth-order (RKF45) integration scheme using the MAPLE software. Achieved results are validated with previous studies in an excellent way. Major outcomes reveal that the magnetic flux reduces the velocity components in the radial, angular, and axial directions, and enhances the fluid temperature. Also, the presence of radiative heat flux is to raise the temperature of fluid. Further, the strength of homogeneous-heterogeneous reactions is useful to diminish the concentration of reaction.

Everything you always wanted to know about SDPD ⋆ ( ⋆ but were afraid to ask)

Abstract: An overview of the smoothed dissipative particle dynamics (SDPD) method is presented in a format that tries to quickly answer questions that often arise among users and newcomers. It is hoped that the status of SDPD is clarified as a mesoscopic particle model and its potentials and limitations are highlighted, as compared with other methods.

Simultaneous impacts of MHD and variable wall temperature on transient mixed Casson nanofluid flow in the stagnation point of rotating sphere

Abstract: A numerical analysis is provided to scrutinize time-dependent magnetohydrodynamics (MHD) free and forced convection of an electrically conducting non-Newtonian Casson nanofluid flow in the forward stagnation point region of an impulsively rotating sphere with variable wall temperature. A single-phase flow of nanofluid model is reflected with a number of experimental formulae for both effective viscosity and thermal conductivity of nanofluid. Exceedingly nonlinear governing partial differential equations (PDEs) subject to their compatible boundary conditions are mutated into a system of nonlinear ordinary differential equations (ODEs). The derived nonlinear system is solved numerically with implementation of an implicit finite difference procedure merging with a technique of quasi-linearization. The controlled parameter impacts are clarified by a parametric study of the entire flow regime. It is depicted that from all the exhibited nanoparticles, Cu possesses the best convection. The surface heat transfer and surface shear stresses in the x- and z-directions are boosted with maximizing the values of nanoparticle solid volume fraction φ and rotation λ. Besides, as both the surface temperature exponent n and the Casson parameter γ upgrade, an enhancement of the Nusselt number is given.

Quadratic convective flow of radiated nano-Jeffrey liquid subject to multiple convective conditions and Cattaneo-Christov double diffusion

Abstract: A nonlinear flow of Jeffrey liquid with Cattaneo-Christov heat flux is investigated in the presence of nanoparticles. The features of thermophoretic and Brownian movement are retained. The effects of nonlinear radiation, magnetohydrodynamic (MHD), and convective conditions are accounted. The conversion of governing equations into ordinary differential equations is prepared via stretching transformations. The consequent equations are solved using the Runge-Kutta-Fehlberg (RKF) method. Impacts of physical constraints on the liquid velocity, the temperature, and the nanoparticle volume fraction are analyzed through graphical illustrations. It is established that the velocity of the liquid and its associated boundary layer width increase with the mixed convection parameter and the Deborah number.

Investigation of Coulomb force effects on ethylene glycol based nanofluid laminar flow in a porous enclosure

Abstract: Forced convection heat transfer of ethylene glycol based nanofluid with Fe 3 O 4 inside a porous medium is studied using the electric field. The control volume based finite element method (CVFEM) is selected for numerical simulation. The impact of the radiation parameter ( R d ), the supplied voltage (△ ψ ), the volume fraction of nanofluid ( φ ), the Darcy number ( Da ), and the Reynolds number ( Re ) on nanofluid treatment is demonstrated. Results prove that thermal radiation increases the temperature gradient near the positive electrode. Distortion of isotherms increases with the enhance of the Darcy number and the Coulomb force.

Mathematical model of micropolar fluid in two-phase immiscible fluid flow through porous channel

Abstract: This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically.

Fallopian tube assessment of the peristaltic-ciliary flow of a linearly viscous fluid in a finite narrow tube

Abstract: The present theoretical assessment deals with the peristaltic-ciliary transport of a developing embryo within a fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of a linearly viscous fluid within a fallopian tubal fluid in a finite two-dimensional narrow tube is developed. The lubrication approximation theory is used to solve the resulting partial differential equation. The expressions for axial and radial velocities, pressure gradient, stream function, volume flow rate, and time mean volume flow rate are derived. Numerical integration is performed for the appropriate residue time over the wavelength and the pressure difference over the wavelength. Moreover, the plots of axial velocity, the appropriate residue time over wavelength, the vector, the pressure difference over wavelength, and the streamlines are displayed and discussed for emerging parameters and constants. Salient features of the pumping characteristics and the trapping phenomenon are discussed in detail. Furthermore, a comparison between the peristaltic flow and the peristaltic-ciliary flow is made as the special case. Relevance of the current results to the transport of a developing embryo within a fallopian tubal fluid from ampulla to the intramural in the fallopian tube is also explored. It reveals the fact that cilia along with peristalsis helps to complete the required mitotic divisions while transporting the developing embryo within a fallopian tubal fluid in the human fallopian tube.

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das' nanofluid model

Abstract: The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls (wavy and undulation numbers) are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.

3D Casson nanofluid flow over slendering surface in a suspension of gyrotactic microorganisms with Cattaneo-Christov heat flux

Abstract: A mathematical model is proposed to execute the features of the non-uniform heat source or sink in the chemically reacting magnetohydrodynamic (MHD) Casson fluid across a slendering sheet in the presence of microorganisms and Cattaneo-Christov heat flux. Multiple slips (diffusion, thermal, and momentum slips) are applied in the modeling of the heat and mass transport processes. The Runge-Kutta based shooting method is used to find the solutions. Numerical simulation is carried out for various values of the physical constraints when the Casson index parameter is positive, negative, or infinite with the aid of plots. The coefficients of the skin factors, the local Nusselt number, and the Sherwood number are estimated for different parameters, and discussed for engineering interest. It is found that the gyrotactic microorganisms are greatly encouraged when the dimensionless parameters increase, especially when the Casson fluid parameter is negative. It is worth mentioning that the velocity profiles when the Casson fluid parameter is positive are higher than those when the Casson fluid parameter is negative or infinite, whereas the temperature and concentration fields show exactly opposite phenomena.

Nonlocal buckling of embedded magnetoelectroelastic sandwich nanoplate using refined zigzag theory

Abstract: This paper is concerned with a buckling analysis of an embedded nanoplate integrated with magnetoelectroelastic (MEE) layers based on a nonlocal magnetoelectroelasticity theory. A surrounding elastic medium is simulated by the Pasternak foundation that considers both shear and normal loads. The sandwich nanoplate (SNP) consists of a core that is made of metal and two MEE layers on the upper and lower surfaces of the core made of BaTiO3/CoFe2O4. The refined zigzag theory (RZT) is used to model the SNP subject to both external electric and magnetic potentials. Using an energy method and Hamilton’s principle, the governing motion equations are obtained, and then solved analytically. A detailed parametric study is conducted, concentrating on the combined effects of the small scale parameter, external electric and magnetic loads, thicknesses of MEE layers, mode numbers, and surrounding elastic medium. It is concluded that increasing the small scale parameter decreases the critical buckling loads.

Effectiveness of Darcy-Forchheimer and nonlinear mixed convection aspects in stratified Maxwell nanomaterial flow induced by convectively heated surface

Abstract: The effect of nonlinear mixed convection in stretched flows of rate-type non-Newtonian materials is described. The formulation is based upon the Maxwell liquid which elaborates thermal relation time characteristics. Nanofluid properties are studied considering thermophoresis and Brownian movement. Thermal radiation, double stratification, convective conditions, and heat generation are incorporated in energy and nanoparticle concentration expressions. A boundary-layer concept is implemented for the simplification of mathematical expressions. The modeled nonlinear problems are computed with an optimal homotopy scheme. Moreover, the Nusselt and Sherwood numbers as well as the velocity, nanoparticle concentration, and temperature are emphasized. The results show opposite impacts of the Deborah number and the porosity factor on the velocity distribution.

Comparison and analysis of two Coulomb friction models on the dynamic behavior of slider-crank mechanism with a revolute clearance joint

Abstract: The objective of this study is to investigate the effects of the Coulomb dry friction model versus the modified Coulomb friction model on the dynamic behavior of the slider-crank mechanism with a revolute clearance joint. The normal and tangential forces acting on the contact points between the journal and the bearing are described by using a Hertzian-based contact force model and the Coulomb friction models, respectively. The dynamic equations of the mechanism are derived based on the Lagrange equations of the first kind and the Baumgarte stabilization method. The frictional force is solved via the linear complementarity problem (LCP) algorithm and the trial-and-error algorithm. Finally, three numerical examples are given to show the influence of the two Coulomb friction models on the dynamic behavior of the mechanism. Numerical results show that due to the stick friction, the slider-crank mechanism may exhibit stick-slip motion and can balance at some special positions, while the mechanism with ideal joints cannot.

TiO2-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

Abstract: The TiO2-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem (BVP). The BVP is analytically solved with the homotopy analysis method (HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO2 nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO2 nanoparticles increases. This confirms the fact that the occurrence of the TiO2 nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased. An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water, while the Nusselt number of the nanofluid is larger than that of pure water. However, both the parameters increase if the magnetic field intensity increases.

Modeling biomembranes and red blood cells by coarse-grained particle methods

Abstract: In this work, the previously developed coarse-grained (CG) particle models for biomembranes and red blood cells (RBCs) are reviewed, and the advantages of the CG particle methods over the continuum and atomistic simulations for modeling biological phenomena are discussed. CG particle models can largely increase the length scale and time scale of atomistic simulations by eliminating the fast degrees of freedom while preserving the mesoscopic structures and properties of the simulated system. Moreover, CG particle models can be used to capture the microstructural alternations in diseased RBCs and simulate the topological changes of biomembranes and RBCs, which are the major challenges to the typical continuum representations of membranes and RBCs. The power and versatility of CG particle methods are demonstrated through simulating the dynamical processes involving significant topological changes, e.g., lipid self-assembly vesicle fusion and membrane budding.

Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields

Abstract: The bending and free vibration of a rotating sandwich cylindrical shell are analyzed with the consideration of the nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields by use of the first-order shear deformation theory (FSDT) of shells. The governing equations of motion and the corresponding boundary conditions are established through the variational method and the Maxwell equation. The closed-form solutions of the rotating sandwich cylindrical shell are obtained. The effects of geometrical parameters, volume fractions of carbon nanotubes, applied voltages on the inner and outer piezoelectric layers, and magnetic and thermal fields on the natural frequency, critical angular velocity, and deflection of the sandwich cylindrical shell are investigated. The critical angular velocity of the nanocomposite sandwich cylindrical shell is obtained. The results show that the mechanical properties, e.g., Young’s modulus and thermal expansion coefficient, for the carbon nanotube and matrix are functions of temperature, and the magnitude of the critical angular velocity can be adjusted by changing the applied voltage.

Fluid flow driven along microchannel by its upper stretching wall with electrokinetic effects

Abstract: We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method (HAM) to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.

Numerical simulation of chemically reactive Powell-Eyring liquid flow with double diffusive Cattaneo-Christov heat and mass flux theories

Abstract: A numerical study is reported for two-dimensional flow of an incompressible Powell-Eyring fluid by stretching the surface with the Cattaneo-Christov model of heat diffusion. Impacts of heat generation/absorption and destructive/generative chemical reactions are considered. Use of proper variables leads to a system of non-linear dimensionless expressions. Velocity, temperature and concentration profiles are achieved through a finite difference based algorithm with a successive over-relaxation (SOR) method. Emerging dimensionless quantities are described with graphs and tables. The temperature and concentration profiles decay due to enhancement in fluid parameters and Deborah numbers.

Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials

Abstract: The pulsatile electroosmotic flow (PEOF) of a Maxwell fluid in a parallel flat plate microchannel with asymmetric wall zeta potentials is theoretically analyzed. By combining the linear Maxwell viscoelastic model, the Cauchy equation, and the electric field solution obtained from the linearized Poisson-Boltzmann equation, a hyperbolic partial differential equation is obtained to derive the flow field. The PEOF is controlled by the angular Reynolds number, the ratio of the zeta potentials of the microchannel walls, the electrokinetic parameter, and the elasticity number. The main results obtained from this analysis show strong oscillations in the velocity profiles when the values of the elasticity number and the angular Reynolds number increase due to the competition among the elastic, viscous, inertial, and electric forces in the flow.

The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates

Abstract: The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes (SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton’s principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection, geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate.

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

Abstract: A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then, the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is calculated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally, the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

Static deformation of a multilayered one-dimensional hexagonal quasicrystal plate with piezoelectric effect

Abstract: Quasicrystals (QCs) are sensitive to the piezoelectric (PE) effect. This paper studies static deformation of a multilayered one-dimensional (1D) hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal (PQC) plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.

Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

Abstract: The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar´e perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve. When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.

One-dimensional dynamic equations of a piezoelectric semiconductor beam with a rectangular cross section and their application in static and dynamic characteristic analysis

Abstract: Within the framework of continuum mechanics, the double power series expansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degenerated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic behaviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.

Semi-analytic solution of Eringen's two-phase local/nonlocal model for Euler-Bernoulli beam with axial force

Abstract: Eringen’s two-phase local/nonlocal model is applied to an Euler-Bernoulli nanobeam considering the bending-induced axial force, where the contribution of the axial force to bending moment is calculated on the deformed state. Basic equations for the corresponding one-dimensional beam problem are obtained by degenerating from the three-dimensional nonlocal elastic equations. Semi-analytic solutions are then presented for a clamped-clamped beam subject to a concentrated force and a uniformly distributed load, respectively. Except for the traditional essential boundary conditions and those required to be satisfied by transferring an integral equation to its equivalent differential form, additional boundary conditions are needed and should be chosen with great caution, since numerical results reveal that non-unique solutions might exist for a nonlinear problem if inappropriate boundary conditions are used. The validity of the solutions is examined by plotting both sides of the original integro-differential governing equation of deflection and studying the error between both sides. Besides, an increase in the internal characteristic length would cause an increase in the deflection and axial force of the beam.

Lattice Boltzmann simulation of MHD natural convection in a cavity with porous media and sinusoidal temperature distribution

Abstract: The lattice Boltzmann method (LBM) is used to simulate the effect of magnetic field on the natural convection in a porous cavity. The sidewalls of the cavity are heated sinusoidally with a phase derivation, whereas the top and bottom walls are thermally insulated. Numerical simulation is performed, and the effects of the pertinent parameters, e.g., the Hartmann number, the porosity, the Darcy number, and the phase deviation, on the fluid flow and heat transfer are investigated. The results show that the heat transfer is affected by the temperature distribution on the sidewalls clearly. When the Hartmann number is 0, the maximum average Nusselt number is obtained at the phase deviation 90°. Moreover, the heat transfer enhances when the Darcy number and porosity increase, while decreases when the Hartman number increases.

Complex modes and traveling waves in axially moving Timoshenko beams

Abstract: Complex modes and traveling waves in axially moving Timoshenko beams are studied. Due to the axially moving velocity, complex modes emerge instead of real value modes. Correspondingly, traveling waves are present for the axially moving material while standing waves dominate in the traditional static structures. The analytical results obtained in this study are verified with a numerical differential quadrature method.