Sharif Digital Repository

In this paper, an analytical method is presented in order to determine the static bending response of an axisymmetric thin circular/annular plate with different boundary conditions resting on a spatially inhomogeneous Winkler foundation. To this end, infinite power series expansion of the deflection function is exploited to transform the governing differential equation into a new solvable system of recurrence relations. Singular points of the governing equation are effectively treated by applying the Frobenius theorem in the solution, which in turn permits the use of more-general analytical functions to describe the variation of the foundation modulus along the radius of the plate. Moreover,... 

In this paper, the whirling frequencies of simply supported and clamped rotating cylindrical shells surrounded by an elastic foundation are investigated. The Love's shell theory is used along with the Winkler foundation to obtain the governing equations of motion. An exact power series solution is obtained for arbitrary boundary conditions and the results are verified with the literature. Several case studies are performed, and the effect of spinning speed, foundation stiffness, and geometrical dimensions of the cylinder on the whirling frequencies are investigated  

In this paper, strain gradient elasticity formulation for analysis of FG (functionally graded) micro-cylinders is presented. The material properties are assumed to obey a power law in radial direction. The governing differential equation is derived as a fourth order ODE. A power series solution for stresses and displacements in FG micro-cylinders subjected to internal and external pressures is obtained. Numerical examples are presented to study the effect of the characteristic length parameter and FG power index on the displacement field and stress distribution in FG cylinders. It is observed that the characteristic length parameter has a considerable effect on the stress distribution of FG... 

In this paper, free vibration analysis of thin symmetrically laminated skew plates with fully clamped edges is investigated. The governing differential equation for skew plate which is a fourth order partial differential equation (PDE) is obtained by transforming the differential equation in Cartesian coordinates into skew coordinates. Based on the multi-term extended Kantorovich method (MTEKM) an efficient and accurate approximate closed-form solution is presented for the governing PDE. Application of the MTEKM reduces the governing PDE to a dual set of ordinary differential equations. These sets of equations are then solved with infinite power series solution, in an iterative manner until...