Response of beams on elastic foundations to harmonic loads: Closed-form solutions

The Fourier transform is used to derive the steady-state response of an infinite beam resting on a two-parameter elastic foundation under a harmonic concentrated load. The solutions are introduced in closed forms and the inherent damping of the system is considered in the analysis. First, the Fourier transform is used to construct the Green's function of the problem which is then used to obtain an integral representation of the solution. Then, the residues theorem is employed for the resulting integral and closed-form solutions are obtained for various cases of the beam and foundation parameters. The obtained solutions are compared, for some special-cases, with those found in literature and showed full agreement. Finally, the obtained solutions are used to construct corresponding solutions when the applied loading is a concentrated harmonic moment and also when several concentrated harmonic forces and/or moments are applied.