General Analysis of Timoshenko Beams on Elastic Foundation

Abstract

General analytical solutions for stability, free and forced vibration of an axially loaded Timoshenko beam resting on a two-parameter foundation subjected to nonuniform lateral excitation are obtained using recursive differentiation method (RDM). Elastic restraints for rotation and translation are assumed at the beam ends to investigate the effect of support weakening on the beam behavior. However, the effects of rotational inertia and shear stress induced from the axial load are considered. The obtained solutions are verified first and then used to investigate the significance of different parameters on the beam behavior. In addition, solutions of forced vibration are analyzed to highlight the effects of excitation nonhomogeneity on the beam behavior.