Sharif Digital Repository

This paper deals with the study of the small scale effect on the pull-in instability of nano-switches subjected to electrostatic and intermolecular forces. Using Eringen's nonlocal elasticity theory, the nonlocal Euler-Bernoulli beam model is derived through virtual displacement principle. The static governing equation which is extremely nonlinear due to the intermolecular and electrostatic attraction forces is solved numerically by differential quadrature method. The accuracy of the present method is verified by comparing the obtained results with the finite difference method and those in the literatures and very good agreement is obtained. Finally a comprehensive study is carried out to... 

This article presents a study on the thermal buckling behavior of two-dimensional functionally graded microbeams made of porous materials. The material composition varies along thickness and length of the microbeam based on the power law distribution. The microbeam is modeled within the framework of Euler–Bernoulli beam theory. The microbeam is considered having variable material composition along thickness. The equations are derived using the modified couple stress theory and the solving process is based on the generalized differential quadrature method. The validity of the results is shown through comparison of the results with the results of other published research. © 2017 Taylor &... 

Although many researchers have studied the vibration and buckling behavior of porous materials, the behavior of porous nanobeams is still a needed issue to be studied. This paper is focused on the buckling and nonlinear vibration of functionally graded (FG) porous nanobeam for the first time. Nonlinear Von Kármán strains are put into consideration to study the nonlinear behavior of nanobeam based on the Euler–Bernoulli beam theory. The nonlocal Eringen’s theory is used to study the size effects. The mechanical properties of ceramic and metal are used to model the functionally graded material through thickness, and the boundary conditions are considered as clamped–clamped (CC) and simply... 

In this study, a cylindrical microshell stability reinforced by graphene nanoplatelets is investigated while an axial load is applied uniformly. In addition, viscoelastic foundation covers the composite nanostructure. Therefore, the impacts of the small scale parameter are studied while nonlocal strain gradient theory (NSGT) is considered. The present research deals for the first time with the consideration of viscoelastic, strain–stress size-dependent parameters along with taking into account of various boundary conditions (BCs), especially C-F ones put into effect on the proposed theory. The governing equations (G.Eqs) and BCs have been obtained utilizing energy method and solved with... 

The stability analysis of cantilevered curved microtubules in axons regarding various size elements and using the generalized differential quadrature method for solving equations is reported. The impacts of covering MAP Tau proteins along with cytoplasm are taken into account as the elastic medium. Curved cylindrical nanoshell considering thick wall is used to model the microtubules. The factor of length scale (l/R = 0.2) used in modified couple stress theory would result in more accuracy when it comes to comparison with experiments, while alternative theories presented in this paper provide less precise outcomes. Due to the reported precise results, at the lower value of the time-dependent... 

In this article, dynamic equations of a single wheel robot, known as Gyrover, through Lagrange method applying a new approach will be addressed. There is no simplification on the dynamic analysis. Considering any possible differentiable function for the road's curve, the effect of the road's roughness is completely described in the dynamic equation evaluation. Although there are complicated relations between the wheel and rough terrain, due to the efficient generalized coordinate selection, closed form dynamic equation of the motion is derived. Because of the closed form formulation, required time for simulation will be reduced. From the proposed complete model a simplified model for the... 

In this study, a cylindrical microshell stability reinforced by graphene nanoplatelets is investigated while an axial load is applied uniformly. In addition, viscoelastic foundation covers the composite nanostructure. Therefore, the impacts of the small scale parameter are studied while nonlocal strain gradient theory (NSGT) is considered. The present research deals for the first time with the consideration of viscoelastic, strain–stress size-dependent parameters along with taking into account of various boundary conditions (BCs), especially C-F ones put into effect on the proposed theory. The governing equations (G.Eqs) and BCs have been obtained utilizing energy method and solved with... 

In this paper, based on the high-order theory (HOT) of sandwich structures, the response of sandwich cylindrical shells with flexible core and any sort of boundary conditions under a general distributed static loading is investigated. The faces and the core are made of isotropic materials. The faces are modeled as thin cylindrical shells obeying the Kirchhoff–Love assumptions. For the core material, it is assumed to be thick and the in-plane stresses are negligible. The governing equations are derived using the principle of the stationary potential energy. Using harmonic differential quadrature method (HDQM), the equations are solved for deformation components. The obtained results are... 

The buckling analysis of cross-ply laminated conical shell panels with simply supported boundary conditions at all edges and subjected to axial compression is studied. The conical shell panel is a very interesting problem as it can be considered as the general case for conical shells when the subtended angle is set to 2π and also cylindrical panels and shells when the semi-vertex angle is equal to zero. Equations were derived using classical shell theory of Donnell type and solved using generalized differential quadrature method. The results are compared and validated with the known results in the literature. The effects of subtended angle, semi-vertex angle, length, thickness and radius of... 

Three-dimensional free vibration analysis of functionally graded piezoelectric (FGPM) annular plates resting on Pasternak foundations with different boundary conditions is presented. The material properties are assumed to have an exponent-law variation along the thickness. A semi-Analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is utilized to obtain the influences of the Winkler and shearing layer elastic coefficients of the foundations on the non-dimensional natural frequencies of functionally graded piezoelectric annular plates. The analytical solution in the thickness direction can be... 

In this paper, we are concerned with the numerical approximation of stochastic differential equations with discontinuous/nondifferentiable drifts. We show that under one-sided Lipschitz and general growth conditions on the drift and global Lipschitz condition on the diffusion, a variant of the implicit Euler method known as the split-step backward Euler (SSBE) method converges with strong order of one half to the true solution. Our analysis relies on the framework developed in [D. J. Higham, X. Mao and A. M. Stuart, Strong convergence of Euler-type methods for nonlinear stochastic differential equations, SIAM Journal on Numerical Analysis, 40 (2002) 10411063] and exploits the relationship... 

In this study vibration amplitude, frequency and damping of a microbeam is controlled using a RLC block containing a capacitor, resistor and inductor in series with the microbeam. Applying this method all of the considerable characteristics of the oscillatory system can be determined and controlled with no change in the geometrical and physical characteristics of the microbeam. Euler-Bernoulli assumptions are made for the microbeam and the electrical current through the microbeam is computed by considering the microbeam deflection and its voltage. Considering the RLC block, the voltage difference between the microbeam and the substrate is calculated. Two coupled nonlinear partial... 

Neuronal temporal synchronization is one of the key issues in studying binding phenomenon in neural systems. In this paper we consider identical Hindmarsh-Rose neurons coupled over Newman-Watts small-world networks and investigate to what extent the numerical and analytic synchronizing coupling strengths are different. We use the master-stability-function approach to determine the unified coupling strength necessary for analytic synchronization. We also solve the network's differential equations numerically and track the synchronization error and consequently determine the numerical synchronizing coupling parameters. Then, we compare these two values and investigate the influence of various... 

This article aims to study the buckling and free vibrational behavior of axially functionally graded (AFG) nanobeam under thermal effect for the first time. The temperature is considered to be constant and variable along thickness and different boundary conditions. The governing equation is developed using the Hamilton’s principle considering the axial force. The Euler–Bernoulli beam theory is used to model the nanobeam, and Eringen’s nonlocal elasticity theory is utilized to consider the nano-size effect. The generalized differential quadrature method (GDQM) is used to solve the equations. The small-scale parameter, AFG power index, thermal distribution, different functions of temperature... 

The vibration analysis of rotating, functionally graded Timoshenko nano-beams under an in-plane nonlinear thermal loading is studied for the first time. The formulation is based on Eringen's nonlocal elasticity theory. Hamilton's principle is used for the derivation of the equations. The governing equations are solved by the differential quadrature method. The nano-beam is under axial load due to the rotation and thermal effects, and the boundary conditions are considered as cantilever and propped cantilever. The thermal distribution is considered to be nonlinear and material properties are temperature-dependent and are changing continuously through the thickness according to the power-law... 

The linear static elastic-plastic behavior of sandwich cylindrical shell panels under a generally distributed loading with thick flexible core is studied. The core modeling is based on high-order theory of sandwich structures in which the in-plane stresses of the core are neglected. The faces are modeled based on Kirchhoff-Love shell theory. The materials of the faces and the core are assumed to be isotropic with linear work hardening behavior. The incremental Prandtl-Reuss plastic flow theory is used in this analysis. Using the principle of virtual displacements, the governing equations are derived and solved for any sort of boundary conditions based on elastic-plastic harmonic differential... 

The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton’s principle. The small-scale effect has been considered using the nonlocal Eringen’s elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are... 

The vibration analysis of rotating, functionally graded Timoshenko nano-beams under an in-plane nonlinear thermal loading is studied for the first time. The formulation is based on Eringen's nonlocal elasticity theory. Hamilton's principle is used for the derivation of the equations. The governing equations are solved by the differential quadrature method. The nano-beam is under axial load due to the rotation and thermal effects, and the boundary conditions are considered as cantilever and propped cantilever. The thermal distribution is considered to be nonlinear and material properties are temperature-dependent and are changing continuously through the thickness according to the power-law... 

The stability analysis of cantilevered curved microtubules in axons regarding various size elements and using the generalized differential quadrature method for solving equations is reported. The impacts of covering MAP Tau proteins along with cytoplasm are taken into account as the elastic medium. Curved cylindrical nanoshell considering thick wall is used to model the microtubules. The factor of length scale (l/R = 0.2) used in modified couple stress theory would result in more accuracy when it comes to comparison with experiments, while alternative theories presented in this paper provide less precise outcomes. Due to the reported precise results, at the lower value of the time-dependent... 

This is the first research on the thermal buckling analysis of graphene nanoplatelets reinforced composite (GPLRC) doubly curved open cylindrical micropanel in the framework of numerical-based two-dimensional generalized differential quadrature method (2D-GDQM). Additionally, the small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The stresses and strains are obtained using the high-order shear deformable theory (HOSDT). The rule of mixture is employed to obtain varying thermal expansion, and Poisson's ratio, while module of elasticity is computed by modified Halpin-Tsai model. In addition, nonlinear temperature changes along the GPLRC micropanel's thickness...