Free vibration analysis of a beam with an intermediate sliding connection joined by a mass-spring system

Abstract

In the free vibration analysis of beams, the inclusion of an intermediate sliding connection with an attached mass-spring system has not been yet treated. The present paper studies the free vibrations of uniform Euler-Bernoulli beams with an intermediate sliding connection and joined by a mass-spring system. Two different types of beams are considered. The Type 1 is attached with a single-degree-of-freedom mass-spring system and the Type 2 is attached with a two-degree-of-freedom mass-spring system. The ends of both beams are elastically restrained against rotation and translation. First, the eigenvalue problems including differential equations and boundary conditions are introduced. Then, the frequency equation of beam could be found. The roots of this frequency equation, i.e., frequency parameters, for several cases along with mode shapes are presented. Some special cases for the sake of verification are thoroughly investigated.