Sharif Digital Repository

In this paper, free vibration of the micro-cylinder made by functionally graded material stiffened in circumferential direction was investigated based on modified couple stress and first-order shear deformation theories. Modified Couple Stress Theory (MCST) was used to catch size effects in micro scales. By using first-order shear deformation theory and Hamilton's principle, the general equations of motion and corresponding boundary conditions were derived. Free vibration of the structure was investigated by implementing simply-supported boundary condition as a common case. The effects of different parameters, such as dimensionless length scale parameter, distribution of FGM properties,... 

In this study, the numerical simulation of the fluid flow and acoustic field of a supersonic jet is performed by using high-order discretization and the vorticity confinement (VC) method on coarse grids. The three-dimensional Navier-Stokes equations are considered in the generalized curvilinear coordinate system and the high-order compact finite-difference scheme is applied for the space discretization, and the time integration is performed by the fourth-order Runge-Kutta scheme. A low-pass high-order filter is applied to stabilize the numerical solution. The non-reflecting boundary conditions are adopted for all the free boundaries, and the Kirchhoff surface integration is utilized to... 

In this study, a multiplate shear model is developed for dynamic analysis of multilayer graphene sheets with arbitrary shapes considering the interlayer shear effect. By utilizing the model, then some free-vibration analysis is presented. According to the experimental results, the weak interlayer van der Waals interaction cannot maintain the integrity of carbon atoms in adjacent layers. Therefore, it is required that the interlayer shear effect is accounted to study multilayer graphene mechanical behavior. The governing differential equation of motion is derived for the multilayer graphene sheets utilizing a variational approach based on the Kirchhoff plate model. The essential and natural... 

The staggered quantum walk is a type of discrete-time quantum-walk model without a coin which can be generated on a graph using particular partitions of the graph nodes. We design Hamiltonians for potential realization of the staggered dynamics on a two-dimensional lattice composed of superconducting microwave resonators connected with tunable couplings. The naive generalization of the one-dimensional staggered dynamics generates two uncoupled one-dimensional quantum walks; thus more complex partitions need to be employed. However, by analyzing the coherence of the dynamics, we show that the quantumness of the evolution corresponding to two independent one-dimensional quantum walks can be... 

In this paper, a three-dimensional simulation of fully coupled multiphase fluid flow and heat transfer through deforming porous media is presented in the context of EFG mesh-less method. Spatial discretization of the system of governing equations is performed using EFG and a fully implicit finite difference scheme is employed for temporal discretization. Penalty method is used for imposition of essential boundary conditions. The developed numerical tool is employed to simulate two problems of nuclear waste disposal and CO2 sequestration in deep underground strata. The obtained results demonstrate the capability and robustness of the developed EFG code. © 2018 Elsevier Ltd  

This study provides an exact solution for the size dependent buckling and post-buckling behavior of functionally graded (FG) micro-beams with arbitrary boundary conditions which are subjected to combined thermo-mechanical loading. To this end, a theoretical formulation including the effects of size dependency, elastic foundation and uniform temperature distribution is first derived using the modified couple stress theory and through the principle of minimum total potential energy. Next, the nonlinear equations governing bending and stretching behavior of FG micro-beams are uncoupled to a fourth-order ordinary differential equation. Finally, the differential operator method is utilized to... 

By employing the nonlocal continuum field theory of Eringen and Von Karman nonlinear strains, this paper presents an analytical model for linear and nonlinear dynamics analysis of single-walled carbon nanotubes (SWNTs) conveying fluid with different boundary conditions. In the linear analysis the natural frequencies and critical flow velocities of SWNTs are computed. However, in the nonlinear analysis the effect of nonlocal parameter on nonlinear dynamics of cantilevered SWNTs conveying fluid is investigated by using bifurcation diagram, phase plane and Poincare map. Numerical results confirm existence of chaos as well as a period-doubling transition to chaos. Copyright © 2018 Techno-Press,... 

A new resonance phenomenon is demonstrated in waveguide cavities, which simultaneously uses two orthogonal modes (polarizations). This resonance is formed by bouncing waves with similar handedness, between two simple anisotropic metasurfaces having a relative rotation angle. The rotated anisotropic metasurfaces can cross couple the waves from one polarization to the other at the cavity end. The field profile of the resonant mode does not exhibit nodes and antinodes, thus the resonant frequency is not solely determined by the cavity length, unlike common resonators. The resonance condition is theoretically demonstrated from both field and transmission line perspectives, and is validated by... 

In this paper, a two-component Lattice Boltzmann Method (LBM) has been utilized to simulate the natural convection of TiO2-water nanofluid in a curved geometry. The main purpose of this research is to study the effect of nanoparticle size and also boundary conditions on the thermal characteristics of the nanofluid. Furthermore, the effect of Rayleigh number (Ra) and volume fraction of nanoparticles (ϕ) on the average Nusselt number (Nuave) have been investigated. Two different thermal boundary conditions, namely adiabatic and constant temperature, have been considered in the current work for the curved boundaries. The Rayleigh number varies from 103 to 109. Four different sizes, namely 10,... 

A size-dependent formulation for the Euler-Bernoulli nano- and micro-beams made of functionally graded materials (FGMs) is presented. The formulation is developed on the basis of the second strain gradient theory (SSGT). This theory is a powerful non-classical continuum theory capable of capturing the small-scale effects in the mechanical behavior of small-scale structures. To drive the governing equations of motion along with the general form of boundary conditions, the Hamilton principle is utilized. Due to the inhomogeneity through the thickness of functionally graded beams, the two equations which govern the axial and flexural deformations are coupled. In two case studies with different... 

Current design codes provide empirical equations for the drift capacity of unreinforced masonry (URM) walls that are based on results of quasi-static cyclic shear-compression tests. Yet different experimental campaigns have used various approaches of imposing fixed-fixed boundary conditions at the wall top which may affect the test results. This article investigates, by means of numerical simulations, the influence of experimental setups on the force and drift capacities of in-plane loaded URM walls subjected to double-fixed conditions. It is shown that controlling the shear span or the top rotation while keeping the axial force constant leads to very similar results. Controlling the axial... 

Displacement-based assessment procedures require as input reliable estimates of the deformation capacity of all structural elements. For unreinforced masonry (URM) walls, current design codes specify the in-plane deformation capacity as empirical equations of interstory drift. National codes differ with regard to the parameters that are considered in these empirical drift capacity equations, but the inhomogeneity of datasets on URM wall tests renders it difficult to validate the hypotheses with the currently available experimental data. This paper contributes to the future development of such empirical relationships by investigating the sensitivity of the drift capacity to the shear span,... 

The effect of a multiphase fluid, including an arbitrary number of liquid phases, and a functionally graded density fluid on the stability of rotating partially-filled cylindrical shells is investigated. The first-order shear shell theory is used for modeling the structural dynamics of the shell and a 2D model is introduced based on the Navier–Stokes equations, for fluid motion. The multiphase and the functionally graded density fluids are arranged according to the mass density in a steady state condition due to centrifugal forces. Using the boundary conditions between liquid phases and the boundary conditions of the fluid on the cylinder wall, the coupled fluid-structure system model is... 

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... 

In this paper, the dynamics of a viscoelastic plate resting on a viscoelastic Winkler foundation and traversed by a moving mass is studied. The Laplace transform is employed to derive the governing equation of the problem. Thereafter, an analytical-numerical method is proposed in order to determine the dynamic response of the plate. The method is based on transforming the governing partial differential equation into a new solvable system of linear ordinary differential equations. To that extent, the proposed solution proves to be applicable to plates made of any viscoelastic material and with various boundary conditions. Moreover, the moving mass may travel at any arbitrary trajectory with... 

Analytical and molecular dynamics simulation approaches are used in this paper to study free-vibration behavior of multilayer graphene-based nanoresonators considering interlayer shear effect. According to experimental observations, the weak interlayer van der Waals interaction cannot maintain the integrity of carbon atoms in the adjacent layers. Hence, it is vital that the interlayer shear effect is taken into account to design and analyze multilayer graphene-based nanoresonators. The differential equation of motion and the general form of boundary conditions are first derived for multilayer graphene sheets with rectangular shape using the Hamilton’s principle. Then, by pursuing an... 

In this paper, the static pull-in behavior of electrostatically actuated functionally graded (FG) micro-beams resting on an elastic medium is studied using the modified strain gradient (MSG) theory. To this end, the equilibrium equation along with classical and non-classical boundary conditions is obtained by considering the fringing field and elastic foundations effects within the principle of minimum total potential energy. Also, the elastic medium is composed of a shear layer (Pasternak foundation) and a linear normal layer (Winkler foundation). The governing differential equation is solved for cantilever and doubly fixed FG beams using an iterative numerical method. This method is a... 

The present work aims to study the anti-plane scattering of SH-waves by an elastic micro-/nano-fiber which is embedded near the interface between exponentially graded and homogeneous half-spaces incorporating interface effects. The fiber is perfectly bonded to the inhomogeneous medium. It is well-known that traditional elasticity theory is incapable of accounting accurately for the nanoscopic-interfaces and, likewise, inappropriate for the prediction of the behavior of nano-sized structures where the surface-to-volume ratio is remarkably large. In the present study, the interface effects are incorporated using the well-known (Gurtin and Murdoch, 1975) surface elasticity theory which permits... 

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... 

Based on the first-order shear deformation plate theory, two approaches within the extended Kantorovich method (EKM) are presented for a bending analysis of functionally graded annular sector plates with arbitrary boundary conditions subjected to both uniform and non-uniform loadings. In the first approach, EKM is applied to the functional of the problem, while in the second one EKM is applied to the weighted integral form of the governing differential equations of the problem as presented by Kerr. In both approaches, the system of ordinary differential equations with variable coefficients in r direction and the set of ordinary differential equations with constant coefficients in θ direction...