Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Tim...Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.展开更多
Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of th...Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.展开更多
The behavior of a water molecule entering carbon nanotubes （CNTs） is stud- ied. The Lennaxd-Jones potential function together with the continuum approximation is used to obtain the van der Waals interaction between ...The behavior of a water molecule entering carbon nanotubes （CNTs） is stud- ied. The Lennaxd-Jones potential function together with the continuum approximation is used to obtain the van der Waals interaction between a single-walled CNT （SWCNT） and a single water molecule. Three orientations are chosen for the water molecule as the center of mass is on the axis of nanotube. Extensive studies on the variations of force, energy, and velocity distributions axe performed by vaxying the nanotube radius and the orientations of the water molecule. The force and energy distributions are validated by those obtained from molecular dynamics （MD） simulations. The acceptance radius of the nanotube for sucking the water molecule inside is derived, in which the limit of the radius is specified so that the nanotube is favorable to absorb the water molecule. The velocities of a single water molecule entering CNTs axe calculated and the maximum entrance and the interior velocity for different orientations axe assigned and compared.展开更多
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 effect...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.展开更多
The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface e...The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.展开更多
In the present paper, the dynamic stability of multi-walled carbon nanotubes （MW- CNTs） embedded in an elastic medium is investigated including thermal environment effects. To this end, a nonlocal Timoshenko beam mo...In the present paper, the dynamic stability of multi-walled carbon nanotubes （MW- CNTs） embedded in an elastic medium is investigated including thermal environment effects. To this end, a nonlocal Timoshenko beam model is developed which captures small scale effects. Dynamic governing equations of the carbon nanotubes are formulated based on the Timoshenko beam theory including the effects of axial compressive force. Then a parametric study is conducted to investigate the influences of static load factor, temperature change, nonlocal parameter, slenderness ratio and spring constant of the elastic medium on the dynamic stability characteristics of MWCNTs with simply-supported end supports.展开更多
The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Er...The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Eringen's nonlocal elasticity theory, a nonclassical model is developed. Using the Galerkin method(GM), the governing equation which is a nonlinear partial differential equation(NLPDE) of the fourth order is converted to a nonlinear ordinary differential equation(NLODE) in the time domain. Then, the reduced NLODE is solved analytically by means of the homotopy analysis method. At the end, the effects of model parameters as well as the nonlocal parameter on the deflection, nonlinear frequency, and dynamic pull-in voltage are explored.展开更多
A new numerical approach is presented to compute the large deformations of shell-type structures made of the Saint Venant-Kirchhoff and Neo-Hookean materials based on the seven-parameter shell theory.A work conjugate ...A new numerical approach is presented to compute the large deformations of shell-type structures made of the Saint Venant-Kirchhoff and Neo-Hookean materials based on the seven-parameter shell theory.A work conjugate pair of the first Piola Kirchhoff stress tensor and deformation gradient tensor is considered for the stress and strain measures in the paper.Through introducing the displacement vector,the deformation gradient,and the stress tensor in the Cartesian coordinate system and by means of the chain rule for taking derivative of tensors,the difficulties in using the curvilinear coordinate system are bypassed.The variational differential quadrature(VDQ)method as a pointwise numerical method is also used to discretize the weak form of the governing equations.Being locking-free,the simple implementation,computational efficiency,and fast convergence rate are the main features of the proposed numerical approach.Some well-known benchmark problems are solved to assess the approach.The results indicate that it is capable of addressing the large deformation problems of elastic and hyperelastic shell-type structures efficiently.展开更多
Based on the micropolar theory(MPT),a two-dimensional(2 D)element is proposed to describe the free vibration response of structures.In the context of the MPT,a 2 D formulation is developed within the ABAQUS finite ele...Based on the micropolar theory(MPT),a two-dimensional(2 D)element is proposed to describe the free vibration response of structures.In the context of the MPT,a 2 D formulation is developed within the ABAQUS finite element software.The user-defined element(UEL)subroutine is used to implement a micropolar element.The micropolar effects on the vibration behavior of 2 D structures with arbitrary shapes are studied.The effect of micro-inertia becomes dominant,and by considering the micropolar effects,the frequencies decrease.Also,there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales,and this difference decreases when the side length-to-length scale ratio becomes large.展开更多
This paper is aimed to propose a three-dimensional model which would be used for investigation on the mechanical behavior of single-layered zinc oxide nanosheets. To develop this model, molecular mechanics is coupled ...This paper is aimed to propose a three-dimensional model which would be used for investigation on the mechanical behavior of single-layered zinc oxide nanosheets. To develop this model, molecular mechanics is coupled with the density functional theory. Simulating the hexagonal lattices of nanosheets as a hexagonal mechanical structure composed of structural beam elements, the buckling behavior of zinc oxide nanosheets is studied. Effects of different parameters on the stability of armchair and zigzag nanosheets are examined. It is shown that the buckling forces of zigzag nanosheets are slightly greater than those of armchair ones. However, with increasing size of nanosheets the effect of atomic structure on the stability of nanosheets diminishes.By studying the effect of end conditions on the buckling behavior of nanosheets, it is shown the stability of nanosheets is affected significantly by boundary conditions.展开更多
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 ...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.展开更多
Electromechanical carbon nanothermometers are devices that work based on the interactions and relative mo- tions of double-walled carbon nanotubes （DWCNTs）. In this paper, the mechanics of carbon nanotubes （CNTs） ...Electromechanical carbon nanothermometers are devices that work based on the interactions and relative mo- tions of double-walled carbon nanotubes （DWCNTs）. In this paper, the mechanics of carbon nanotubes （CNTs） con- stituting two welt-known configurations for nanothermome- ter, namely shuttle configuration and telescope configuration are fully investigated. Lennard-Jones （LJ） potential func- tion along with the continuum approximation is employed to investigate van der Waals （vdW） interactions between the in- teracting entities. Accordingly, semi-analytical expressions in terms of single integrals are obtained for vdW interactions. Acceptance condition and suction energy are studied for the shuttle configuration. In addition, a universal potential en- ergy is presented for the shuttle configuration consisting of two finite CNTs. Also, for the telescope configuration, ex- tensive studies are performed on the distributions of potential energy and interaction force for various radii and lengths of CNTs. It is found that these geometrical parameters have a considerable effect on the potential energy.展开更多
文摘Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.
文摘Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects.Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral version.In this article,a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal models.This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation.First,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy.Also,in each case,the governing equation is obtained in both strong and weak forms.To solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule.It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes.Also,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.
文摘The behavior of a water molecule entering carbon nanotubes （CNTs） is stud- ied. The Lennaxd-Jones potential function together with the continuum approximation is used to obtain the van der Waals interaction between a single-walled CNT （SWCNT） and a single water molecule. Three orientations are chosen for the water molecule as the center of mass is on the axis of nanotube. Extensive studies on the variations of force, energy, and velocity distributions axe performed by vaxying the nanotube radius and the orientations of the water molecule. The force and energy distributions are validated by those obtained from molecular dynamics （MD） simulations. The acceptance radius of the nanotube for sucking the water molecule inside is derived, in which the limit of the radius is specified so that the nanotube is favorable to absorb the water molecule. The velocities of a single water molecule entering CNTs axe calculated and the maximum entrance and the interior velocity for different orientations axe assigned and compared.
文摘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.
文摘The nonlinear vibrations of viscoelastic Euler-Bernoulli nanobeams are studied using the fractional calculus and the Gurtin-Murdoch theory. Employing Hamilton＇s principle, the governing equation considering surface effects is derived. The fractional integro-partial differential governing equation is first converted into a fractional-ordinary differential equation in the time domain using the Galerkin scheme. Thereafter, the set of nonlinear fractional time-dependent equations expressed in a state-space form is solved using the predictorcorrector method. Finally, the effects of initial displacement, fractional derivative order, viscoelasticity coefficient, surface parameters and thickness-to-length ratio on the nonlinear time response of simply-supported and clamped-free silicon viscoelastic nanobeams are investigated.
文摘In the present paper, the dynamic stability of multi-walled carbon nanotubes （MW- CNTs） embedded in an elastic medium is investigated including thermal environment effects. To this end, a nonlocal Timoshenko beam model is developed which captures small scale effects. Dynamic governing equations of the carbon nanotubes are formulated based on the Timoshenko beam theory including the effects of axial compressive force. Then a parametric study is conducted to investigate the influences of static load factor, temperature change, nonlocal parameter, slenderness ratio and spring constant of the elastic medium on the dynamic stability characteristics of MWCNTs with simply-supported end supports.
文摘The current paper presents a thorough study on the pull-in instability of nanoelectromechanical rectangular plates under intermolecular, hydrostatic, and thermal actuations. Based on the Kirchhoff theory along with Eringen's nonlocal elasticity theory, a nonclassical model is developed. Using the Galerkin method(GM), the governing equation which is a nonlinear partial differential equation(NLPDE) of the fourth order is converted to a nonlinear ordinary differential equation(NLODE) in the time domain. Then, the reduced NLODE is solved analytically by means of the homotopy analysis method. At the end, the effects of model parameters as well as the nonlocal parameter on the deflection, nonlinear frequency, and dynamic pull-in voltage are explored.
文摘A new numerical approach is presented to compute the large deformations of shell-type structures made of the Saint Venant-Kirchhoff and Neo-Hookean materials based on the seven-parameter shell theory.A work conjugate pair of the first Piola Kirchhoff stress tensor and deformation gradient tensor is considered for the stress and strain measures in the paper.Through introducing the displacement vector,the deformation gradient,and the stress tensor in the Cartesian coordinate system and by means of the chain rule for taking derivative of tensors,the difficulties in using the curvilinear coordinate system are bypassed.The variational differential quadrature(VDQ)method as a pointwise numerical method is also used to discretize the weak form of the governing equations.Being locking-free,the simple implementation,computational efficiency,and fast convergence rate are the main features of the proposed numerical approach.Some well-known benchmark problems are solved to assess the approach.The results indicate that it is capable of addressing the large deformation problems of elastic and hyperelastic shell-type structures efficiently.
文摘Based on the micropolar theory(MPT),a two-dimensional(2 D)element is proposed to describe the free vibration response of structures.In the context of the MPT,a 2 D formulation is developed within the ABAQUS finite element software.The user-defined element(UEL)subroutine is used to implement a micropolar element.The micropolar effects on the vibration behavior of 2 D structures with arbitrary shapes are studied.The effect of micro-inertia becomes dominant,and by considering the micropolar effects,the frequencies decrease.Also,there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales,and this difference decreases when the side length-to-length scale ratio becomes large.
文摘This paper is aimed to propose a three-dimensional model which would be used for investigation on the mechanical behavior of single-layered zinc oxide nanosheets. To develop this model, molecular mechanics is coupled with the density functional theory. Simulating the hexagonal lattices of nanosheets as a hexagonal mechanical structure composed of structural beam elements, the buckling behavior of zinc oxide nanosheets is studied. Effects of different parameters on the stability of armchair and zigzag nanosheets are examined. It is shown that the buckling forces of zigzag nanosheets are slightly greater than those of armchair ones. However, with increasing size of nanosheets the effect of atomic structure on the stability of nanosheets diminishes.By studying the effect of end conditions on the buckling behavior of nanosheets, it is shown the stability of nanosheets is affected significantly by boundary conditions.
文摘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.
文摘Electromechanical carbon nanothermometers are devices that work based on the interactions and relative mo- tions of double-walled carbon nanotubes （DWCNTs）. In this paper, the mechanics of carbon nanotubes （CNTs） con- stituting two welt-known configurations for nanothermome- ter, namely shuttle configuration and telescope configuration are fully investigated. Lennard-Jones （LJ） potential func- tion along with the continuum approximation is employed to investigate van der Waals （vdW） interactions between the in- teracting entities. Accordingly, semi-analytical expressions in terms of single integrals are obtained for vdW interactions. Acceptance condition and suction energy are studied for the shuttle configuration. In addition, a universal potential en- ergy is presented for the shuttle configuration consisting of two finite CNTs. Also, for the telescope configuration, ex- tensive studies are performed on the distributions of potential energy and interaction force for various radii and lengths of CNTs. It is found that these geometrical parameters have a considerable effect on the potential energy.
