Dynamic stiffness formulation and its application for a combined beam and a two degree-of-freedom system

This paper is concerned with the dynamic stiffness formulation and its application for a Bernoulli-Euler beam carrying a two degree-of-freedom spring-mass system. The effect of a two degree-of-freedom system kinematically connected to the beam is represented exactly by replacing it with equivalent stiffness coefficients, which are added to the appropriate stiffness coefficients of the bare beam. Numerical examples whose results are obtained by applying the Wittrick-Williams algorithm to the total dynamic stiffiness matrix are given and compared with published results. Applications of the theory include the free vibration analysis of frameworks carrying two degree-of-freedom spring-mass systems.