Adomian Decomposition Method for Solving a Cantilever Beam of Varying Orientation with Tip Mass

[+] Author and Article Information
Mustafa Yaman

Department of Mechanical Engineering, Ataturk University, Erzurum, Turkeymyaman@atauni.edu.tr

J. Comput. Nonlinear Dynam 2(1), 52-57 (Jun 01, 2006) (6 pages) doi:10.1115/1.2389167 History: Received February 09, 2006; Revised June 01, 2006

A uniform cantilever beam of varying orientation with a tip mass at the free end can be used as a basic model of many practical structures such as flexible robot arm or antenna mast. The aim of the study described here is to investigate the influence of the orientation effect on the natural frequency of the cantilever beam carrying a tip mass. An analytic solution is obtained by using the Adomian decomposition method. The accuracy of the Adomian decomposition method with a varying number of terms in the series is investigated by comparing its results with those generated by the finite element method.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Cantilever beam of varying orientation with a concentrated mass

Grahic Jump Location
Figure 3

The convergence test for the Adomian’s decomposition solution, as a function of the number of terms in the series: (a) first mode; (b) second mode; (c) third mode

Grahic Jump Location
Figure 2

Modes of vibration: (a) ANSYS; (b) Adomian decomposition method




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