Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation

Abstract

The aim of this paper is to reveal the effectiveness of Adomian decomposition method (ADM) and differential transform method (DTM) on free vibrations of axial-loaded Timoshenko beams resting on viscoelastic foundation. The effects of axial compressive load, modulus of subgrade reaction and foundation damping on natural frequencies of beam model are studied using various boundary conditions. The results of DTM and ADM are tabulated with exact results that obtained from analytical formulations where an excellent agreement is observed. Moreover, the dynamic stiffness method (DSM) which uses the exact mode shapes is applied to verify the analytical results. The accuracy of mathematical tools DTM and ADM is demonstrated by several numerical examples. The first four mode shapes are depicted. It is highlighted that application of DTM, ADM and DSM can be extended without any difficulties for free vibrations of beam assembly structures that resting on viscoelastic foundation. © 2018 Karabuk University