Adomian Polynomials for Nonlinear Response of Supported Timoshenko Beams Subjected to a Moving Harmonic Load

This paper investigates the steady-state responses of a Timoshenko beam of infinite length supported by a nonlinear viscoelastic Pasternak foundation subjected to a moving harmonic load. The nonlinear viscoelastic foundation is assumed to be a Pasternak foundation with linear-plus-cubic stiffness and viscous damping. Based on Timoshenko beam theory, the nonlinear equations of motion are derived by considering the effects of the shear deformable beams and the shear modulus of foundations at the same time. For the first time, the modified Adomian decomposition method (ADM) is used for solving the response of the beam resting on a nonlinear foundation. By employing the standard ADM and the modified ADM, the nonlinear term is decomposed, respectively. Based on the Green’s function and the theorem of residues presented, the closed form solutions for those linear iterative equations have been determined via complex Fourier transform. Numerical results indicate that two kinds of ADM predict qualitatively identical tendencies of the dynamic response with variable parameters, but the deflection of beam predicted by the modified ADM is smaller than that by the standard ADM. The influence of the shear modulus of beams and foundation is investigated. The numerical results show that the deflection of Timoshenko beams decrease with an increase of the shear modulus of beams and that of foundations.