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Shock and Vibration
Volume 20, Issue 4, Pages 601-617

An Improved Beam Element for Beams with Variable Axial Parameters

Peng He, Zhansheng Liu, and Chun Li

School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang, China

Received 21 April 2012; Revised 4 December 2012; Accepted 14 January 2013

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.


The traditional beam element was improved to consider the variable axial parameters. The variable axial parameters were formulated in terms of a power series, and the general forms of elementary mass and stiffness matrices which depend on the power order were derived. The mass and stiffness matrices of the improved beam element were obtained in terms of an elementary matrix series. The beam elements for various tapered beams and a beam under linearly axial temperature distribution were derived. The vibrations of the beams with various taper shapes were studied and the variations of natural frequencies and modal shapes were investigated. A uniform beam under linearly axial temperature distribution was modeled and studied. The influences of axial temperature difference on the natural frequencies and modal shapes were investigated. Results show that the improved beam element could consider the variable axial parameters of beam conveniently.