In this paper, a unified analytical approach is proposed to investigate vibrational behavior of functionally graded shells. Theoretical formulation is established based on Sanders’ thin shell theory. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stoke's transformation. Material properties are assumed to be graded in the thickness direction according to different volume fraction functions such as power-law, sigmoid, double-layered and exponential distributions. A FGM cylinderical shell made up of a mixture of ceramic and metal is considered. The Influence of some commonly used boundary conditions, the effect of changes in shell geometrical parameters and variations of volume fraction functions on the vibration characteristics are studied by comparing the results from the present theory with those from the First order Shear Deformation Theory (FSDT). Furthermore, the results obtained for a number of particular cases show good agreement with those available in the open literature. The simplicity and the capability of the present method are also discussed.

In the present work, free vibration analysis of the square sandwich plate with functionally graded (FG) porous face sheets and isotropic homogenous core is performed under Various boundary conditions. For this purpose, the material properties of the sandwich plate are supposed to vary continuously through the thickness direction according to the volume fraction of constituents defined with the modified rule of the mixture including porosity volume fraction with three different types of porosity distribution over the cross-section. Furthermore, a hyperbolic shear displacement theory is used in the kinematic relation of the FG porous sandwich plate, and the equations of motion are derived utilizing Hamilton’ s principle. Analytical solutions are achieved for free vibration analysis of square sandwich plates with FG porous face sheets under Various boundary conditions, i. e. combinations of clamped (C), simply supported (SS), and free (F) edges are presented. Several parametrical studies are conducted to examine the effects of porosity volume fraction, type of porosity distribution model, lay-up scheme, side to thickness ratio, and boundary conditions on the free vibration of the FG sandwich plates. Finally, it is concluded that the investigated parameters have significant effects on the free vibration of the FG sandwich plates and the negative effects of porosity may be reduced by adopting suitable values for said parameters, considerably.

In this paper, a thermoelasticity solution for steady state response of thick cylinders which are subjected to pressure and external heat flux in inner surface is presented. Displacement field obeys the kinematics of the first order shear deformation theory (FSDT).It is assumed that the temperature varies both along the length and the thickness. The variation of the temperature occurs linearly through the thickness. Using energy method, the equilibrium equations and general boundary conditions are derived for thecylinder. Based on the developed analytical solution, adequatenumerical results are depicted to provide an insight into the influence of the thermal and mechanical loads and boundary conditions on thermo-mechanical behavior of cylinder. Results show that shear stresses arenotice able at boundaries; moreover, temperature, displacement fields and stresses are stronglydependedon length. Furthermore, the capability of the proposed method to solve any axisymmetrically cylindrical shells with general boundary conditions and thermo-mechanical loadingis proven.

In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy is achieved. Solution of VIM for natural frequencies and mode shapes of a Timoshenko beam is compared to the available exact closed-form solution and numerical results of differential quadrature method (DQM). The accuracy of VIM is approximately the same as exact solution and much better than the DQM for solving the free vibration of a Timoshenko beam. Also, convergence speed and simplicity of this method is more than the other two methods because it works with polynomial at the first iteration. Thus, VIM can be used for solving the complicate engineering problems which do not have analytical solution.

In this study, axisymmetric buckling of annular orthotropic graphene sheet embedded in a Winkler– Pasternak elastic medium is scrutinized for different boundary conditions based on non-local elasticity theory. With the aid of principle of virtual work, the non-local governing equations are derived based on First-order Shear Deformation Theory (FSDT). Differential Quadrature Method (DQM) is also used to solve equilibrium equations. Edges of Nano-plate might be restrained by different combinations of free, simply supported or clamped boundary conditions. To confirm results, comparison of studies is made between results obtained and available solutions in the literature. Finally, a detailed parametric study is conducted to investigate the impact of small scale effects, surrounding elastic medium, boundary conditions and geometrical parameters on critical buckling load. The main goal of this work is to study the effect of Various non-local parameters on the buckling load of annular Nano-plate for different boundary conditions, Winkler and shear foundation parameters, annularity and thickness-to-radius ratios. It is seen that for Nano-plates without an elastic foundation, the impact of thickness on buckling load does not depend on values of non-local parameter and annularity. Results also show that impact of elastic basis on the buckling load is independent of small scale effects.