Sharif Digital Repository

Dynamic and stability analysis of non-uniform Timoshenko beam under axial loads is carried out. In the first case of study, the axial force is assumed to be perpendicular to the shear force, while for the second case the axial force is tangent to the axis of the beam column. For each case, a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending was obtained. The parameters of the frequency equation were determined for various boundary conditions. Several illustrative examples of uniform and non-uniform beams with different boundary conditions such as clamped supported, elastically supported, and free end mass have been... 

A polynomial expansion approach to the extraction of guided and leaky modes in layered structures including dielectric waveguides and periodic stratified media is proposed. To verify the method we compared the results of analysis of a typical test case with those reported in the literature and found good agreement. Polynomial expansion is a nonharmonic expansion and does not involve harmonic functions or intrinsic modes of homogenous layers. This approach has the benefit of leading to algebraic dispersion equations rather than to a transcendental dispersion equation; therefore, it will be easier to use than other methods such as the argument principle method, the reflection pole method, and... 

In this article, the dynamics of plates under influence of relatively large masses, moving along an arbitrary trajectory on the plate surface is considered. The method consists of transformation of the governing equation into a series of eigenfunctions, which satisfy the boundary conditions of the plate. The method presented in this investigation is general and can be applied to general moving mass and moving force systems as well. Furthermore, the article shows that the response of structures due to moving mass, which has often been neglected in the past, must be properly taken into account because it often differs significantly from the moving force model. © 2001 Published by Elsevier... 

In this article, the edge-zone equation of Mindlin-Reissner plate theory, for composite plates laminated of transversely isotropic layers is studied. Analytical solutions are obtained for both circular sector and completely circular plates with various boundary conditions. The boundary-layer function and its effect on the stresses are numerically studied. Effects of plate thickness and boundary conditions are investigated. The results for circular and completely circular plates are exactly the same as those of rectangular plates in our previous work. Therefore, this boundary layer phenomenon seems to be geometry independent. © Springer-Verlag 2000  

The dissimilar wedge with finite radius under antiplane shear deformation is analyzed. The finite Mellin transform is used to solve the governing differential equation. By simply letting the wedge radius approaches infinity, the solution is obtained  

In the current research, a comprehensive analytical technique is presented to evaluate the non-Fourier thermal behavior of a 3-D hollow sphere subjected to arbitrarily-chosen space and time dependent boundary conditions. The transient hyperbolic thermal diffusion equation is driven based upon the Cattaneo-Vernotte (C-V) model and nondimensionalized using proper dimensionless parameters. The conventional procedure of separation of variables is applied for solving the 3-D hyperbolic heat conduction equation with general boundary conditions. In order to handle the time dependency of the boundary conditions, Duhamel's theorem is employed. Furthermore, for the purpose of demonstrating 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... 

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... 

Kinematic boundary condition is usually used when dealing with transient free-surface flow problems in isotropic media. When dealing with anisotropic problems, a transformation can transform the anisotropic media to an equivalent isotropic media for seepage analysis, but the kinematic boundary condition cannot be used directly in the transformed media. A generalization of the kinematic boundary condition along any arbitrary direction is derived for use in the transformed domain for general three-dimensional anisotropic problems. A boundary element method for solving transient free-surface seepage problems is developed and the treatment of the proposed kinematic boundary condition in the... 

The present study examines Alternating Current (AC) electroosmotic flows in a parallel plate microchannel subject to constant wall temperature. Numerical method consists of a central finite difference scheme for spatial terms and a forward difference scheme for the temporal term. Asymmetric boundary conditions are assumed for Poison-Boltzmann equation for determining the electric double layer (EDL) potential distribution. The potential distribution is then used to evaluate the velocity distribution. The velocity distribution is obtained by applying slip boundary conditions on the walls which accounts for probable hydrophobicity of surfaces. After determining the velocity distribution... 

A semi-analytical solution for rotating axisymmetric disks made of functionally graded materials was previously proposed by Hosseini Kordkheili and Naghdabadi [1]. In the present work the solution is employed to study thermoelastic creep behavior of the functionally graded rotating disks with variable thickness in to the time domain. The rate type governing differential equations for the considered structure are derived and analytically solved in terms of rate of strain as a reduced to a set of linear algebraic equations. The advantage of this method is to avoid simplifications and restrictions which are normally associated with other creep solution techniques in the literature. The thermal... 

This study presents the bending analysis of functionally graded conical panels under transverse compression with various boundary conditions. Equations was derived using first order shear deformation theory (FSDT) and solved using generalized differential quadrature (GDQ) method. Using this method results in the capability of studying any combinations of boundary conditions on four edges of the panel. Results are compared and validated with the results available in the literature. Effect of boundary conditions, volume fractions, panel length, semi-vertex angle and subtended angle on deflection of the panel was investigated  

This is a theoretical study dealing with longitudinal gaseous slip flow forced convection between a periodic bunch of microcylinders arranged in regular array. The selected geometry has applications in microscale pin fin heat sinks used for cooling of microchips. The flow is considered to be hydrodynamically and thermally fully developed. 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 and three of the boundary conditions... 

The present work develops direct graded boundary integral equation formulation for behavior investigation of the inhomogeneous media made of functionally graded materials. The isoparametric boundary elements, the elastostatic governing equations and a weighted residual technique are implemented with the material characteristics that vary continuously along a given dimension. The resulting algorithm is capable of solving the quasistatic problems for elastic functionally graded media with a variety of the boundary conditions and loadings. The inhomogeneous media is made of a ceramic-metal mixture, in which the material properties vary continuously according to a power law graded distribution... 

The objective of this paper is to derive the mathematical model of two-dimensional heat conduction at the inner and outer surfaces of a hollow cylinder which are subjected to a time-dependent periodic boundary condition. The substance is assumed to be homogenous and isotropic with time-independent thermal properties. Duhamel's theorem is used to solve the problem for the periodic boundary condition which is decomposed by Fourier series. In this paper, the effects of the temperature oscillation frequency on the boundaries, the variation of the hollow cylinder thickness, the length of the cylinder, the thermophysical properties at ambient conditions, and the cylinder involved in some... 

This paper presents a finite element method (FEM) free and forced lateral vibration analysis of beams made of functionally graded materials (FGMs). The temperature dependency of material properties along with damping had not previously been taken into account in vibration analysis. In the present study, the material properties were assumed to be temperature-dependent, and were graded in the thickness direction according to a simple power law distribution of the volume fractions of the constituents. The natural frequencies were obtained for functionally graded (FG) beams with various boundary conditions. First, an FG beam was assumed to be isotropic (metal rich) and the results were compared... 

Free vibration of laminated micro-plates with arbitrary geometry and boundary conditions consisting of several micro-layers with free sliding/frictional sliding/perfect interfaces is of interest. The inter-layer bond in the direction normal to the interfaces is perfect, and thus the corresponding displacement component is continuous across the interfaces. The mentioned in-plane interface conditions may be realized by varying the stiffness of the sliding inter-layer spring of vanishing thickness. For free sliding and perfect interface conditions the stiffness→0 and a, respectively. Couple stress theory as a useful higher order continuum theory is utilized to formulate the problem.... 

The selection of interface boundary conditions between porous-medium and clear-fluid regions is very important for the wide range of engineering applications. In this paper, the difference between two common types of fluid flow interfacial conditions between clear fluid and porous medium is analyzed in detail. These two types of fluid flow interfacial condition are stress-jump and stress-continuity conditions. The effects of porosity on these types of interface condition are studied. The results are presented for different Reynolds numbers in the range 1–40, porosity equal to 0.4 and 0.8 and Darcy number Da=5×10-4. In this study, the Darcy–Brinkmann–Forchheimer model is used to model the...