Modified and Simplified Sectional Flexibility of a Cracked Beam

Joint Authors

Wang, Chih-Shiung
Lee, Lin-Tsang

Source

Journal of Applied Mathematics

Issue

Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-16, 16 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2011-10-13

Country of Publication

Egypt

No. of Pages

16

Main Subjects

Mathematics

Abstract EN

This paper presents a new sectional flexibility factor to simulate the reduction of the stiffness of a single-edge open cracked beam.

The structural model for crack of the beam is considered as a rotational spring which is related to the ratio of crack depth to the beam height, a/h.

The mathematical model of this single-edge open crack beam is considered as an Euler-Bernoulli beam.

The modified factor, f(a/h), derived in this paper is in good agreement with previous researchers' results for crack depth ratio a/h less than 0.5.

The natural frequencies and corresponding mode shapes for lateral vibration with different types of single-edge open crack beams can then be evaluated by applying this modified factor f(a/h).

Using the compatibility conditions on the crack and the analytical transfer matrix method, the numerical solutions for natural frequencies of the cracked beam are obtained.

The natural frequencies and the mode shapes with crack at different locations are obtained and compared with the latest research literature.

The numerical results of the proposed cracked beam model obtained by this method can be extended to construct frequency contour.

The natural frequencies measured from field can be used in solving the inverse problem to identify cracks in structures.

American Psychological Association (APA)

Wang, Chih-Shiung& Lee, Lin-Tsang. 2011. Modified and Simplified Sectional Flexibility of a Cracked Beam. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-993362

Modern Language Association (MLA)

Wang, Chih-Shiung& Lee, Lin-Tsang. Modified and Simplified Sectional Flexibility of a Cracked Beam. Journal of Applied Mathematics No. 2012 (2012), pp.1-16.
https://search.emarefa.net/detail/BIM-993362

American Medical Association (AMA)

Wang, Chih-Shiung& Lee, Lin-Tsang. Modified and Simplified Sectional Flexibility of a Cracked Beam. Journal of Applied Mathematics. 2011. Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-993362

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-993362