Sharif Digital Repository

Thermal post-buckling behavior of a geometrically imperfect/perfect piezo-magnetic nano-scale beams made of two-phase composites is analyzed in the present paper based on nonlocal elasticity theory. For the first time, the material properties of the nanobeam are considered as functions of piezoelectric phase percentage. All previous investigations on piezo-magnetic nanobeams neglect the effect of geometrical imperfection which is very important since the nanobeams are not always ideal or perfect. The post-buckling problem of such nanobeams is solved by introducing an analytical approach to derive buckling temperatures. The present solution is simple and easily understandable. For both... 

In this paper the free vibration of single walled carbon nanopeapods encapsulating C60 molecules is considered. The nanopeapod is embedded in an elastic medium and clamped at both ends. The Euler-Bernoulli beam model is used for the carbon nanotube and the C60 molecules are considered as lumped masses attached to the beam. Based on the nonlocal elasticity theory the governing equation of motion is derived and the resonance frequencies of the nanopeapod are obtained. The effects of small scale, foundation stiffness and ratio of the fullerenes' mass to the nanotube's mass on the frequencies are studied and some conclusions are drawn  

In this paper a shell formulation is proposed for analyzing the torsional instability of carbon nano-peapods (CNPs), i.e., the hybrid structures composed of C60 fullerenes encapsulated inside carbon nanotubes (CNTs), based on the nonlocal elasticity theory. The nonlocal elasticity theory, as a well-known non-classical continuum theory, is capable to capture small scale effects which appear due to the discontinuities in nano-structures. Based on the derived formulation, the critical torsional moments for a pristine (10,10) CNT and C60@ (10,10) CNP are investigated as case studies. The results for the (10,10) CNT are compared with those of the available molecular dynamics simulations in the... 

The paper investigates the effects of fluid flow on the static and dynamic behaviors of electrostatically actuated carbon nanotubes using nonlocal elasticity theory. The influences of various parameters of fluid flow including fluid viscosity, velocity, mass and temperature on the mechanical behaviors of the carbon nanotubes under static and step DC voltages are studied using this theory. The results computed from the nonlocal elasticity theory are compared with those estimated using the classical elasticity theorem and the outcomes demonstrate the applicability of the electrostatically actuated carbon nanotubes as nano sensors and nano actuators in nanofluidic systems. The nanosystem can be... 

The equilibrium governing equations of nonlocal anisotropic thin-walled circular cylindrical shell under combined axial compressive force, torsional load, and external pressure are explicitly derived. This is accomplished by appropriately combining the equilibrium equations and the strain-displacement relations according to Flügge's shell theory and the stress-stain equations of Eringen's nonlocal elasticity theory. An analytical solution for the buckling of the shells is presented by using the complex method. This model is validated by a good agreement between the results given by the present model and available data in the literature. Furthermore, the model is utilized to elucidate the... 

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 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... 

This paper aims to present an explicit relation for thermoelastic damping in nanobeams capturing the small-scale effects on both the continuum mechanics and heat conduction domains. To incorporate small-scale effects, the coupled equations of motion and heat conduction are obtained by employing the nonlocal elasticity theory and the dual-phase-lag heat conduction model. Adopting simple harmonic forms for transverse deflection and temperature increment and solving the governing equations, real and imaginary parts of the frequency are extracted. According to the complex frequency approach, a closed-form size-dependent expression for evaluating thermoelastic damping in nanobeams is derived. To... 

A novel non-classical continuum model for pull-in analysis of multilayer graphene sheets (MLGSs) is developed to consider the effect of shear interaction between layers based on the nonlocal elasticity theory. The equation governing the motion and corresponding boundary conditions of electrostatically actuated MLGSs are obtained based on the nonlocal shear multiplate theory. The Galerkin method along with the first mode shapes for clamped and cantilever MLGSs together with the method of parameter expansion is used to obtain closed-form expressions of the normalized frequency and time history response. In addition, molecular dynamics (MD) simulations are carried out to validate the pull-in... 

In recent years, extensive experiments have shown that classical continuum theory cannot predict the behavior of mechanical microstructures with small size. To accurately design and analyze micro- and nano-electro-mechanical systems, size-dependent continuum theories should be used. These theories model micro- and nano-electro-mechanical systems with higher accuracy because they include size-dependent parameters. In this paper, polysilicon nano-beam is modeled using modified couple stress and Eringen's nonlocal elasticity theories. First, partial differential equations governing the vibration of nano-beams are converted to a one D.O.F. differential equations using Galerkin method, resulting... 

The objective of this paper is to investigate dynamical pull-in behavior of an electrostatic actuated nano-device based on Eringen's nonlocal elasticity theory. The Euler–Bernoulli beam model is used to establish the dynamic equation of motion of the nano-device subjected to both electrostatic and intermolecular forces. The nanobeam is considered with axially immovable ends and the geometrically nonlinearity due to mid-plane stretching is incorporated to the model as well. A new intermolecular attractive force model based on the macroscopic interactions of a circular cross section nanobeam and a flat surface is presented for the carbon nanotube based nano-device. The nonlinear static... 

This study presents analysis on the vibration behavior of the two-dimensional functionally graded (2D-FG) nano and microbeams which are made of two kinds of porous materials for the first time, based on Timoshenko beam theory. The material of the nano and microbeams is modeled as 2D-FGMs according to the power law. The Eringen's nonlocal elasticity and the modified couple stress theories are used, respectively in case of nano and microbeams. The boundary conditions are considered as clamped (CC), simply supported (SS), clamped–simply supported (CS), and cantilever (CF). The governing equations are solved using the generalized differential quadrature method (GDQM). The effects of FG power... 

In this article, the vibration frequency of an orthotropic nanoplate under the effect of temperature change is investigated. Using nonlocal elasticity theory, governing equations are derived. Based on the generalized differential quadrature method for cantilever and propped cantilever boundary conditions, the frequencies of orthotropic nanoplates are considered and the obtained results are compared with valid reported results in the literature. The effects of temperature variation, small scale, different boundary conditions, aspect ratio, and length on natural nondimensional frequencies are studied. The present analysis is applicable for the design of rotating and nonrotating nano-devices... 

In this article, free vibration behavior of a rotating nano/microcircular plate constructed from functionally graded magneto-elastic material is simulated with the first-order shear deformation theory. For the sake of comparison, the nonlocal elasticity theory and the modified couple stress theory are employed to implement the small size effect in the natural frequencies behavior of the nano/microcircular plate. The governing equations of motion for functionally graded magneto-elastic material nano/microcircular plates are derived based on Hamilton’s principle; comparing the obtained results with those in the literature, they are in a good agreement. Finally, the governing equations are... 

This article intends to examine thermoelastic damping (TED) in circular cylindrical nanoshells by considering small-scale effect on both structural and thermal areas. To fulfill this aim, governing equations are extracted with the aid of nonlocal elasticity theory and dual-phase-lag (DPL) heat conduction model. Circular cylindrical shell is also modeled on the basis of Donnell–Mushtari–Vlasov (DMV) equations for thin shells. By inserting asymmetric simple harmonic oscillations of nanoshell into motion, compatibility and heat conduction equations, the size-dependent thermoelastic frequency equation is obtained. By solving this equation and deriving the frequency of nanoshell affected by... 

The present article intends to provide a size-dependent generalized thermoelasticity model and closed-form solution for thermoelastic damping (TED) in cylindrical nanoshells. With the aim of incorporating size effect within constitutive relations and heat conduction equation, nonlocal elasticity theory and Guyer–Krumhansl (GK) heat conduction model are exploited. Donnell–Mushtari–Vlasov (DMV) equations are also employed to model the cylindrical nanoshell. By adopting asymmetric simple harmonic form for oscillations of nanoshell and merging the motion, compatibility and heat conduction equations, the nonclassical frequency equation is extracted. By solving this eigenvalue problem and... 

Based on the first-order shear deformation (FSD) model and nonlocal elasticity theory, the simultaneous effects of shear and small scale on the nonlinear vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams are investigated for the first time. To this end, the governing equations of bending and stretching with von Kármán geometric nonlinearity are decoupled into one fourth-order partial differential equation in terms of transverse deflection. A closed-form solution of the nonlinear natural frequency, which can be used in conceptual design and optimization algorithms of FG- CNTRC beams with different boundary conditions, is developed using a hybrid... 

Based on the first-order shear deformation (FSD) model and nonlocal elasticity theory, the simultaneous effects of shear and small scale on the nonlinear vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams are investigated for the first time. To this end, the governing equations of bending and stretching with von Kármán geometric nonlinearity are decoupled into one fourth-order partial differential equation in terms of transverse deflection. A closed-form solution of the nonlinear natural frequency, which can be used in conceptual design and optimization algorithms of FG- CNTRC beams with different boundary conditions, is developed using a hybrid...