Sharif Digital Repository

The free longitudinal vibration of tapered nanowires is investigated in the context of nonlocal continuum theory. The problem is studied for the nanowires with linearly varied radii under fixedfixed and fixedfree boundary conditions. In order to assess the problem in a more general form, a perturbation technique is proposed based on the Fredholm alternative theorem. The natural frequencies, corresponding mode shapes, and phase velocities of the tapered nanowires are derived analytically up to the second-order perturbation for different boundary conditions. The predicted results by the perturbation technique are successfully verified with those of the exact solution. The obtained results... 

Recently, an approximate formalism [Opt. Express 23, 2764, (2015)] called diffractive interface theory has been reported for the fast analysis of the optical response of metasurfaces, subwavelength two-dimensional periodic arrays. In this method, the electromagnetic boundary conditions are derived using the susceptibility distribution of the metasurface, such that the analysis of metasurface is possible without solving any eigenvalue equation inside the grating layer. In this paper, we modify the boundary conditions to achieve more accurate results. In addition, in this paper, correct Fourier factorization rules are also applied leading to faster convergence rate. The obtained results are... 

In the present investigation, the buckling of generally laminated conical shells with various boundary conditions subjected to axial pressure is studied using an analytical approach. The governing equations are obtained using classical shell theory with Donnell assumptions in strain–deformation relations and the principle of minimum potential energy. The differential equations are solved using trigonometric functions in circumferential and power series in longitudinal directions. All types of boundary conditions can be applied in this method. The results are compared and validated with the results available in the literature, and good agreement is observed. Finally, the effects of the... 

In the present study, free vibrations of single walled carbon nanotubes (SWCNT) on an elastic foundation is investigated by nonlocal theory of elasticity with both beam and shell models. The nonlocal boundary conditions are derived explicitly and effectiveness of nonlocal parameter appearing in nonlocal boundary conditions is studied. Also it is demonstrated that the beam model is comparatively incapable of capturing size effects while shell model captures size effects more precisely. Moreover, the effects of some parameters such as mechanical properties, foundation stiffness, length and radius ratios on the natural frequencies are studied and some conclusions are drawn  

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... 

An existing hydroelastic model is extended for a flat plate subjected to a compression force with spiral spring boundary conditions during water entry. Both vertical and oblique impacts of the plate into calm water are investigated. A longitudinal strip of the plate is analyzed by fully coupling hydrodynamic pressure with elastic responses. Hydrodynamic pressure is determined by potential flow theory and plate deflections are expressed in terms of dry normal modes. The plate deflections are validated through comparison with available asymptotic models, semi-analytical and experimental results. The effect of compression force on the plate deflection is investigated at the midpoint considering... 

The characteristic boundary conditions are applied and assessed for the solution of incompressible inviscid flows. The two-dimensional incompressible Euler equations based on the artificial compressibility method are considered and then the characteristic boundary conditions are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. A fourth-order compact finite-difference scheme is used to discretize the resulting system of equations. The solution methodology adopted is more suitable for this assessment because the Euler equations and the high-accurate numerical scheme applied are quite sensitive to the treatment of boundary... 

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... 

We numerically solve the Navier-Stokes equations to study the rarefied gas flow in short micro-and nanoscale channels. The inlet boundary conditions play a critical role in the structure of flow in short channels. Contrary to the classical inlet boundary conditions, which apply uniform velocity and temperature profiles right at the real channel inlet, we apply the same inlet boundary conditions, but at a fictitious position far upstream of the real channel inlet. A constant wall temperature incorporated with suitable temperature jump is applied at the channel walls. Our solutions for both the classical and extended inlet boundary conditions are compared with the results of other available... 

Based on the Euler–Bernoulli beam model and the modified strain gradient theory, the size-dependent forced vibration of sandwich microbeams with a functionally graded (FG) core is presented. The equation of motion and the corresponding classical and nonclassical boundary conditions are derived using the Hamilton’s principle. An exact solution of the governing equation is developed for sandwich beams with various boundary conditions and subjected to an arbitrarily distributed harmonic transverse load. Finally, parametric studies are presented to investigate the effects of geometric ratios, length scale parameters, power index, boundary conditions, layup, and thickness of the FG layer on the... 

The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flowsolver. The spatial derivative terms of the systemof equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried... 

In this study, the supersonic and choked subsonic flows through micro/nano channels are investigated using direct simulation Monte Carlo (DSMC) method. The supersonic case is simulated at different Knudsen numbers covering slip to transition flow regimes, while the effects of inlet Mach and back pressure are studied in details. The inlet/outlet pressure boundary conditions are suitably implemented benefiting from the basics of characteristics theory. A behavior similar to the one predicted by the Fanno theory is observed here; i.e., the supersonic flow velocity decelerates up to a choking condition where any further increase in Knudsen number is impossible unless strong normal/oblique shocks... 

A new strategy for radiation loss reduction in curved slab waveguides is presented. The proposed strategy is based on the proper modification of the boundary conditions at the core-to-cladding interface, whereupon extremely thin conductive nanolayers with non-zero surface conductance are imposed. The obtained numerical results show a noticeable decrease in the overall loss level. © 2008 The Institution of Engineering and Technology  

The supersonic flutter analysis of simply supported FG cylindrical shell for different sets of in-plane boundary conditions is performed. The aeroelastic equations of motion are constructed using Love's shell theory and von Karman-Donnell-type of kinematic nonlinearity coupled with linearized first-order potential (piston) theory. The material properties are assumed to be temperature-dependant and graded across the thickness of the shell according to a simple power law. The temperature distribution is assumed to vary in the thickness direction and is obtained by solving the steady-state heat conduction equation. The pre-stresses due to the thermal and mechanical loadings are obtained by... 

In this paper using classical beam theory, the dynamical governing differential equations of a vibrating shaft are derived then by using lumped parameter technique and method of transfer matrix (TM) the induced eigen value problem is solved. In calculating natural frequencies of a vibrating shaft under different boundary conditions, primarily the shaft was divided into number of segments. In each segment different number of lumped properties like mass, damping and flexibility on overall massless elastic or rigid shaft were applied. One of the aims of this study was to find out the optimum value for number of segments under different aforementioned conditions. In order to estimate the natural... 

A numerical modeling procedure was used to quantify calibration chamber size and boundary effects for cone penetration testing in sand. In the numerical analyses, chamber diameter and boundary conditions were varied to investigate the effects of chamber size and boundary conditions on cone tip resistance. These analyses show that, for loose sand, a chamber-to-cone diameter ratio of 33 is sufficient for the boundaries to have no influence on the cone tip measurements. However, for very dense sand, the numerical analyses show that the chamber-to-cone diameter ratio should be more than 100 to ensure that boundaries have no influence on cone tip measurements. Numerical analysis indicates that,... 

A new finite-volume-based finite-element method using the quadratic elements is developed in the present study, to analyze the flow in micro and nano sizes with higher-order slip boundary conditions. The method is applied to gaseous flow in micro and nanoscale-channels. The developed method is carried out over a wide range of Knudsen numbers, which cover not only the continuum slip flow regime with 0≤Kn≤0.1 but also it entire the range of transient regime with 0.1