Paper Title:
Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method
  Abstract

In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler–Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

  Info
Periodical
Chapter
Chapter 22: Metrology and Measurement
Edited by
Wu Fan
Pages
4532-4536
DOI
10.4028/www.scientific.net/AMM.110-116.4532
Citation
K. Torabi, J. N. Dastgerdi, S. Marzban, "Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method", Applied Mechanics and Materials, Vols. 110-116, pp. 4532-4536, 2012
Online since
October 2011
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$32.00
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