Stability and free vibration of functionally graded tapered Timoshenko beam-columns on two parameter elastic foundation

Abstract

In this paper, the effect of two parametric elastic foundations on the stability and free vibration behaviour of functionally graded (FG) Euler (EB) and Timoshenko beams (TB) in the presence of conservative axial loads is examined. In Timoshenko beam, both shear deformation and rotary inertia effects are taken into account. The governing equations and boundary conditions are derived using the variational principles and presented in a matrix form. Differential Quadrature Element Method of fist order (DQEM) is used to solve the equations. Many examples and comparisons are presented in order to emphasize the influence of elastic foundation, beam taper, boundary conditions and the material properties. Finally the results are compared with the results given by the other authors using the closed form and other numerical techniques.