The study of beam-mass systems with varying degrees of complexity has been carried out by many investigators using different approaches [1-4].Compared to the conventional finite element method, the dynamic stiffness method (DSM) has been widely used in the vibration analysis of beam structures.The main advantage using the DSM is to give exact results for all natural frequencies and mode shapes without making any approximation due to the use of the dynamic stiffness matrix, which is a frequency dependent matrix having both mass and stiffness properties together rather than two separate mass and stiffness matrices.