Analytical Solution for Free Vibration Analysis of Beam on Elastic Foundation with Different Support Conditions

Analytical solutions for free vibration analyses of a beam on elastic foundation are obtained for different support conditions. The analytical solutions are applied on three different axially loaded cases, namely; (1) one end clamped, the other end simply supported; (2) both ends clamped, and (3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load, N, acting on the beam to Euler buckling load, N-r. The analytical solutions give results which are in excellent agreement with the variational iteration method (VIM) and homotopy perturbation method (HPM) results available in the literature for the particular problem considering all the cases provided in this study and the differential transform method (DTM) results available in the literature for the clamped-pinned case.