Abstract
This study investigates the dynamical behavior of an axially moving beam with elastic foundation under viscous damping. The beam is taken to be simply supported at the ends. Axial speed of beam is assumed to be time‐dependent function about a relatively low mean constant speed. The motion of axially moving beam in the term of transverse vibrations is expressed in the fourth‐order linear and homogeneous partial differential equations with variable coefficients. The governing equations of motion are solved by using the two timescales perturbation method together with the Fourier expansion method. The sum and difference‐type resonances are taken to examine the stability of the system. The influence of the parameters such as damping and stiffness of foundation on the transverse amplitude response of the system is seen. It is found out that the system is stable with the increase in damping.