in this paper, free vibration of an Euler-Bernoulli beam with variable cross-section resting on elastic foundation and under axial tensile force is considered. Beam’s constant height and exponentially varying width yields variable cross-section. The problem is handled for three different boundary conditions: clamped-clamped, simply supported-simply supported and clamp-free beams. First, the equ...

in this paper, the nonlinear conjugate map based on the conjugate hasofer-lind and rackwitz- fiessler (chl-rf) method is applied to evaluate the reliability index using first order reliability method of the embedded noanocompsite beam, which is made from polymer reinforced with carbon nanotubs (cnts). the structure is simulated with timoshenko beam model. the mori-tanaka model is applied for ca...

In this paper, the nonlinear conjugate map is applied based on the conjugate Hasofer-Lind and Rackwitz- Fiessler (CHL-RF) method to evaluate the reliability index using the first order reliability method of the embedded nanocomposite beam, which is made of a polymer reinforced with carbon nanotubes (CNTs). The structure is simulated with the Timoshenko beam model. The Mori-Tanaka model is appli...

Introduction.-The purpose of this note is to advance the theory of the following problem: An elastic beam of infinite length, loaded inside a finite region, rests on a yielding foundation. It is asked how much the results of this theory are influenced by alterations of the assumptions concerning the physical nature of the foundation. As it is known, in engineering the assumption is made that at...

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equati...

In this study, the buckling and free vibration of Timoshenko beams resting on variable elastic foundation analyzed by means of a new finite element formulation. The Winkler model has been applied for elastic foundation. A two-node element with four degrees of freedom is suggested for finite element formulation. Displacement and rotational fields are approximated by cubic and quadratic polynomia...