International Journal of Aerospace and Lightweight Structures

doi: 10.3850/S2010428612000396

On the Use of Differential Transformation Method for Free Vibration Analysis of Euler-Bernoulli Beams with General Elastically End Restraints

Nuttawit Wattanasakulpong¹ and Variddhi Ungbhakorn^{2 1}Department of Mechanical Engineering, Mahanakorn University of Technology, Nong Chok, Bangkok, 10530, Thailand. nuttawit mut@hotmail.com ²Department of Mechanical Engineering, Chulalongkorn University, Bangkok, 10330, Thailand. v_ungbhakorn@yahoo.com

ABSTRACT

The differential transformation method is used to find natural frequencies and mode shapes of Euler-Bernoulli beams in this paper. The beams which are supported by various types of elastically end restraints are considered. The method demonstrates many advantages in terms of rapid convergence, high accuracy, and computational stability. Unlike some approximate approaches which require correctly assumed admissible functions at the early stage of their analysis, the differential transformation method gives all natural frequencies and their mode shapes without any frequency missing. The significant aspects of boundary conditions and spring constants which affect considerably natural frequencies and mode shapes of the beams are taken into investigation. The proficiency of the mathematical models provided in this paper is verified numerically by comparisons with some available results in the open literature.

Keywords: Euler-Bernoulli beam, Free vibration, Natural frequency, Mode shape, Differential transformation method.

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