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Shock and Vibration
Volume 20, Issue 3, Pages 357-367

The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

Gürkan Şcedilakar

Department of Mechanical Engineering, Atatürk University, 25240 Erzurum, Turkey

Received 19 June 2012; Revised 4 October 2012; Accepted 19 October 2012

Copyright © 2013 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.