Analytical solution considering the tangential effect for an infinite beam on a viscoelastic Pasternak foundation

Abstract In this study, the dynamic response of an infinite beam resting on a Pasternak foundation subjected to inclined travelling loads was developed in the form of the analytical solution wherein the tangential effect between the beam and foundation and the damping were taken into consideration. Three parameters were used to model the mechanical resistance of the viscoelastic Pasternak foundation, one of them accounts for the compressive stress in the soil, the other accounts for the shearing effect of soils, and the last one accounts for the damping of the foundation. By contrast, the Pasternak model is more realistic than the Winkler model that just considers the compressive resistance of soil. In the paper, the tangential effect between the beam and foundation was simulated by a series of separate horizontal springs, the damping was also considered to obtain the dynamic response under forced vibration. The theory of elasticity and Newton's laws were used to derive the governing equation. To simplify the partial-differential equation to an algebraic equation, the double Fourier transformation was used wherein the analytical solution in the frequency domain for the dynamic response of the beam is obtained. And its inversion was adopted to convert the integral representation of the solution into the time domain. The degraded solution was then utilized to verify the validity of the proposed solution. Finally, the Maple mathematical software was used for further discussion. The solution proposed in this study can be a useful tool for practitioners.