Journal of Applied Mathematics

Modified and Simplified Sectional Flexibility of a Cracked Beam

Chih-Shiung Wang and Lin-Tsang Lee

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 543828, 16 pages.

Dates
First available in Project Euclid: 17 October 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1350479402

Digital Object Identifier
doi:10.1155/2012/543828

Zentralblatt MATH identifier
1334.74097

Citation

Wang, Chih-Shiung; Lee, Lin-Tsang. Modified and Simplified Sectional Flexibility of a Cracked Beam. J. Appl. Math. 2012 (2012), Article ID 543828, 16 pages. doi:10.1155/2012/543828. https://projecteuclid.org/euclid.jam/1350479402


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