Vibration Analysis of a Coupled Beam System Carrying Any Number of Sprung Masses

Abstract

There are a large number of papers in the literature dealing with the free vibration analysis of single/multi-span uniform beam with multiple spring-mass systems, but that of coupled multi-span beams with any number of spring-mass systems is rare. In this paper, an approach based on finite element analysis is presented to analyze the free vibration of coupled beams with spring-mass attachments. Firstly, the equation of motion of the beam system with attachments is established by conventional finite element method. Secondly, the natural frequencies and the associated mode shapes are obtained from the generalized eigenvalue problem. It is found that the results from the proposed method agree well with those from analytical methods in the literature. Finally, the mode localization and frequency loci veering phenomena of a weakly coupled beam system with multiple spring-mass systems are investigated. Studies show that for weakly coupled beam system with attachments, the mode localization and loci veering will occur once there is a disorder in the system.