0
Technical Briefs

A Note on the Use of Approximate Solutions for the Bending Vibrations of Simply Supported Cracked Beams

[+] Author and Article Information
L. Rubio

Department of Mechanical Engineering, University Carlos III of Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain

J. Fernández-Sáez1

Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spainppfer@ing.uc3m.es

1

Corresponding author.

J. Vib. Acoust 132(2), 024504 (Mar 17, 2010) (6 pages) doi:10.1115/1.4000779 History: Received February 14, 2009; Revised August 07, 2009; Published March 17, 2010; Online March 17, 2010

The main goal of this note is to discuss the applicability of approximate closed-form solutions to evaluate the natural frequencies for bending vibrations of simply supported Euler–Bernoulli cracked beams. From the well-known model, which considers the cracked beam as two beams connected by a rotational spring, different approximate solutions are revisited and compared with those found by a direct method, which has been chosen as reference.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Variation in natural frequencies with crack severity for a crack located at β=0.20; (—) direct method, (−−) perturbation method (Eq. 13), (⋅×⋅) Zhong and Oyadiji method (Eq. 27), and (−◇−) Ritz method: (a) first, (b) second, (c) third, and (d) fourth modes

Grahic Jump Location
Figure 2

Variation in natural frequencies with crack severity for a crack located at β=0.40; (—) direct method, (−−) perturbation method (Eq. 13), (⋅×⋅) Zhong and Oyadiji method (Eq. 27), and (−◇−) Ritz method: (a) first, (b) second, (c) third, and (d) fourth modes

Grahic Jump Location
Figure 3

Crack severity values for which the solution differs from the direct (reference) solution with less than 5%; (−−) ωi calculated from Eq. 13 and (−×−) ωi calculated from Eq. 27: (a) first, (b) second, (c) third, and (d) fourth modes

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In