Paper Info
Title
Modified and Simplified Sectional Flexibility of a Cracked Beam.
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.
Year
DOI
Venue
2012
10.1155/2012/543828
JOURNAL OF APPLIED MATHEMATICS
Field
DocType
Volume
Transfer-matrix method (optics),Compatibility (mechanics),Stiffness,Mathematical analysis,Mode (statistics),Inverse problem,Beam (structure),Vibration,Normal mode,Mathematics
Journal
2012
ISSN
Citations 
PageRank 
1110-757X
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Chih-Shiung Wang100.34
Lin-Tsang Lee200.68