Response of beams on nonlinear viscoelastic foundations to harmonic moving loads

The response of infinite beams supported by nonlinear viscoelastic foundations subjected to harmonic moving loads is studied. A straightforward solution technique applicable in the frequency domain is presented in this paper. The governing equations are solved using a perturbation method in conjunction with complex Fourier transformation. A closed-formed solution is presented in an integral form based on the presented Green’s function and the theorem of residues is used for the calculation of integrals. The solution is directed to compute the deflection and bending moment distribution along the length of the beam. A parametric study is carried out and influences of the load speed and frequency on the beam responses are investigated. It is found that for an excitation frequency of Ω there exist superharmonics of 3Ω O(ε), 5Ω O(ε2), …, (2n − 1) × Ω O(εn−1), n = 1, 2, …