Dynamic stiffness vibration analysis of an elastically connected three-beam system

An exact dynamic stiffness method is developed for predicting the free vibration characteristics of a three-beam system, which is composed of three non-identical uniform beams of equal length connected by innumerable coupling springs and dashpots. The Bernoulli–Euler beam theory is used to define the beams’ dynamic behaviors. The dynamic stiffness matrix is formulated from the general solutions of the basic governing differential equations of a three-beam element in damped free vibration. The derived dynamic stiffness matrix is then used in conjunction with the automated Muller root search algorithm to calculate the free vibration characteristics of the three-beam systems. The numerical results are obtained for two sets of the stiffnesses of springs and a large variety of interesting boundary conditions.