Exact solutions for Timoshenko beams on elastic foundations using Green's functions

Wang, C.M.; Lam, K.Y.; He, X.Q.

Publication

Exact solutions for Timoshenko beams on elastic foundations using Green's functions

Wang, C.M.; Lam, K.Y.;
He, X.Q.

Abstract

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