Sharif Digital Repository

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses  

Modeling the behavior of suspended particles in gaseous phase is important for diverse reasons; e.g. aerosol is usually the main subject of CFD simulations in clean rooms. Additionally, to determine the rate and sites of deposition of particles suspended in inhaled air, the motion of the particles should be predicted in lung airways. Meanwhile there are two basically different approaches to simulate the behavior of particles suspension, Lagrangian and Eulerian approaches. This study compares the results of these two approaches on simulating the same problem. An in-house particle tracking code was developed to simulate the motion of particles with Lagrangian approach. In order to simulate the... 

Recently, an approximate boundary condition [Opt. Lett. 38, 3009 (2013)] was proposed for fast analysis of onedimensional periodic arrays of graphene ribbons by using the Fourier modal method (FMM). Correct factorization rules are applicable to this approximate boundary condition where graphene is modeled as surface conductivity. We extend this approach to obtain the optical properties of two-dimensional periodic arrays of graphene. In this work, optical absorption of graphene squares in a checkerboard pattern and graphene nanodisks in a hexagonal lattice are calculated by the proposed formalism. The achieved results are compared with the conventional FMM, in which graphene is modeled as a... 

In this work, a general semi-analytical method for the determination of the elastic fields within an anisotropic homogeneous elastic solid with an inclined edge or interior crack is developed. In this method, the displacement field is represented as a sum of a function and a finite series of functions with unknown coefficients. The functions are constructed in such a way that all the essential homogeneous and inhomogeneous boundary conditions are satisfied exactly and, moreover, the displacement discontinuity across the crack faces as well as the exact singular behaviour of the stress field at the crack-tip are captured. The unknown coefficients are determined by utilizing the principle of... 

In this article, we find a lower bound for the blow-up time of solutions to some nonlinear parabolic equations under Robin boundary conditions in bounded domains of Rn  

The present investigation is devoted to the fully developed slip flow mixed convection in vertical microducts of two different cross sections, namely, polygon, with circle as a limiting case, and rectangle. The two axially constant heat flux boundary conditions of H1 and H2 are considered in the analysis. The velocity and temperature discontinuities at the boundary are incorporated into the solutions using the first-order slip boundary conditions. The method considered is mainly analytical in which the governing equations in cylindrical coordinates along with the symmetry conditions and finiteness of the flow parameter at the origin are exactly satisfied. The first-order slip boundary... 

Electroosmosis is the main mechanism for flow generation in lab-on-a-chip (LOC) devices. The temperature rise due to the Joule heating phenomenon, associated with the electroosmosis, may be detrimental for samples being considered in LOCs. Hence, a complete understanding of the heat transfer physics associated with the electroosmotic flow is of high importance in design and active control of LOCs. The objective of the present study is to estimate the temperature rise and the thermal entry length in electroosmotic flow through rectangular microchannels, having potential applications in LOC devices. Along this line, the power-law rheological model is used to account for non-Newtonian behavior... 

In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the... 

This paper presents the dynamic response of uniform Timoshenko beams with arbitrary boundary conditions using Dynamic Green Function. An exact and direct modeling technique is stated to model beam structures with arbitrary boundary conditions subjected to the external load that is an arbitrary function of time t and coordinate x and the concentrated moving load. This technique is based on the Dynamic Green Function. The effect of different boundary conditions, load, and other parameters is assessed. Finally, some numerical examples are shown to illustrate the efficiency and simplicity of the new formulation based on the Dynamic Green Function  

Consideration is given to the buoyancy effects on the fully developed gaseous slip flow in a vertical rectangular microduct. Two different cases of the thermal boundary conditions are considered, namely uniform temperature at two facing duct walls with different temperatures and adiabatic other walls (case A) and uniform heat flux at two walls and uniform temperature at other walls (case B). The rarefaction effects are treated using the firstorder slip boundary conditions. By means of finite Fourier transform method, analytical solutions are obtained for the velocity and temperature distributions as well as the Poiseuille number. Furthermore, the threshold value of the mixed convection... 

Thermal load simulation and sensitivity analysis are performed for a building in Tehran by numerical means. A heat conduction equation of the walls, together with appropriate convection and radiation boundary conditions, is simulated numerically to compute temperature distributions in the walls. This research proposes a heat balance method, coupled with a bulk model, to calculate the building thermal load. In the first step, the results of the building thermal load for weather data of Tehran are compared and validated with those of Carrier HAP software, and a good agreement is found between them. The building thermal load depends on the boundary conditions of the building. The influence of... 

This paper presents vibration and buckling analysis of functionally graded beams with different boundary conditions, using reproducing kernel particle method (RKPM). Vibration of simple Euler-Bernoulli beam using RKPM is already developed and reported in the literature. Modeling of FGM beams using theoretical method or finite element technique is not evolved with accurate results for power law form of FGM with large power of "n" value so far. Accuracy of the RKPM results is very good and is not sensitive to n value. System of equations of motion is derived using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of the beam are taken into account using... 

Modified couple stress theory is a size-dependent theorem capturing the micro/nanoscale effects influencing the mechanical behaviors of the micro- and nanostructures. In this paper, it is applied to investigate the nonlinear vibration of carbon nanotubes under step DC voltage. The vibration, natural frequencies and dynamic pull-in characteristics of the carbon nanotubes are studied in detail. Moreover, the effects of various boundary conditions and geometries are scrutinized on the dynamic characteristics. The results reveal that application of this theory leads to the higher values of the natural frequencies and dynamic pull-in voltages  

Accurate description of wall-bounded turbulent flows requires a fine grid near walls to fully resolve the boundary layers. We consider a locally simplified transport model using an assumed near-wall viscosity profile to project the wall boundary conditions using the boundary transfer method. Related coefficients are obtained numerically. By choosing a near-wall viscosity profile, we derive an analytic wall function, which significantly reduces the CPU costs. The performance of this wall function is compared to other near-wall treatments proposed in the literature for two frequently used benchmark cases: near-equilibrium channel flow and flow over a backward-facing step with separation and... 

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential... 

The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin... 

Within elasticity theory, the reduced form of a displacement field is obtained for general cross-ply composite laminates subjected to a bending moment. The firstorder shear deformation theory of plates and Reddy's layerwise theory are then utilized to determine the global deformation parameters and the local deformation parameters appearing in the displacement fields, respectively. For a special set of boundary conditions an elasticity solution is developed to verify the validity and accuracy of the layerwise theory. Finally, various numerical results are presented within the layerwise theory for edge-effect problems of several cross-ply laminates under the bending moment. The results... 

This is a theoretical study that extends a classical method of treating the convection heat transfer in complex geometries to gaseous slip flow forced convection in microchannels with H1 thermal boundary condition. Through this line, the momentum and energy equations in cylindrical coordinates are made dimensionless. Afterward, solutions are presented that exactly satisfy the dimensionless differential equations along with the symmetry condition and finiteness of the flow parameter at the origin. The first-order slip boundary conditions are then applied to the solution utilizing the least squares matching method. Though the method is general enough to be applied to almost any arbitrary cross... 

During the year, due to weather conditions, the temperature fluctuations at surface level cause problems in underground pipes as a result of freezing water. One of the best prevention strategies is the use of polyurethane floor insulation for keeping the temperature of clay above zero degrees Celsius. In this study to calculate the minimum thickness of polyurethane insulation layer, the differential equation of energy is solved based on principle of separation of variables using imaginary eigenvalues for consistency with the temperature distribution in multi-layer consist of asphalt, gravel and polyurethane with finite thickness and clay as a semiinfinite medium with periodic thermal... 

The purpose of this paper is to present efficient and accurate analytical expressions for deflection of a shape memory polymer (SMP) beam employing Euler-Bernoulli beam theory in a thermomechanical SMP cycle. Material behavior is considered using a recently 3D thermodynamically consistent constitutive model available in literature. In different steps of an SMP thermomechanical cycle, closed form expressions for internal variables variations, stresses and beam curvature distribution are presented. We show that during the cooling process, stored strains evolve to fix the temporary shape and then during the heating process they relax to recover the permanent shape. Effects of applying external...