Green’s Functions for Timoshenko Beam Problems

In this paper, a unified formulation is given for the bending, buckling and vibration problems of uniform Timoshenko and Euler-Bernoulli beams resting on various models of elastic foundation. Canonical Green’s functions have been derived for these beams which can be readily used to furnish exact solutions. In addition to elucidating the behaviour of the beams, the exact solutions serve as important benchmark results for checking the convergence and accuracy of various solutions obtained from numerical methods.