Free transversal vibration analysis of cable using Adomian decomposition method

The Adomian decomposition method is employed in this paper to investigate the free vibration of cable consisting of two uniform sections. Each section is considered a substructure which can be modeled using ADM. applying boundary and continuity conditions, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions are presented. The computed results agree well with those analytical and numerical results given in the literature. These results indicate that the present analysis is accurate and provides an efficient, reliable and systematic procedure which is simple and more straightforward than the other modal analysis. Also the effect of amount of mass and spring stiffness at the boundary on variation of natural frequencies is obtained and an effective procedure is suggested for encountering these kinds of problems.