In this paper, vibration analysis of multiple-stepped Bernoulli-Euler and Timoshenko beams carrying point masses is presented analytically for various boundary conditions. Each attached element is considered to have both translational and rotational inertias. The method of solution is “transfer matrix method” which is based on the changes in the vibration modes at the vicinity of any discontinu...

In this paper, a simple and efficient element is proposed for the free vibration buckling analysis of FGM beams. This formulating, based on Timoshenko beam theory. The assumption constant shear strain in reduces number unknowns addition to improving efficiency new element. performance evaluated with help several benchmark tests. First, accuracy convergence rate response are investigated separat...

Collocation methods are popular in providing numerical approximations to complicated governing equations owing to their simplicity in implementation. However, point collocation methods have limitations regarding accuracy and have been modified upon with the application of B-spline approximations. The present study reports the stress and deformation behavior of shear deformable functionally grad...