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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
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