Modified and Simplified Sectional Flexibility of a Cracked Beam
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/543828 |
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| _version_ | 1832551445010841600 |
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| author | Chih-Shiung Wang Lin-Tsang Lee |
| author_facet | Chih-Shiung Wang Lin-Tsang Lee |
| author_sort | Chih-Shiung Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-257fa15b11004491983b9358281616e4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-257fa15b11004491983b9358281616e42025-02-03T06:01:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/543828543828Modified and Simplified Sectional Flexibility of a Cracked BeamChih-Shiung Wang0Lin-Tsang Lee1Department of Applied Mathematics, National Chung Hsing University, Taichung 402, TaiwanDepartment of Applied Mathematics, National Chung Hsing University, Taichung 402, TaiwanThis 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.http://dx.doi.org/10.1155/2012/543828 |
| spellingShingle | Chih-Shiung Wang Lin-Tsang Lee Modified and Simplified Sectional Flexibility of a Cracked Beam Journal of Applied Mathematics |
| title | Modified and Simplified Sectional Flexibility of a Cracked Beam |
| title_full | Modified and Simplified Sectional Flexibility of a Cracked Beam |
| title_fullStr | Modified and Simplified Sectional Flexibility of a Cracked Beam |
| title_full_unstemmed | Modified and Simplified Sectional Flexibility of a Cracked Beam |
| title_short | Modified and Simplified Sectional Flexibility of a Cracked Beam |
| title_sort | modified and simplified sectional flexibility of a cracked beam |
| url | http://dx.doi.org/10.1155/2012/543828 |
| work_keys_str_mv | AT chihshiungwang modifiedandsimplifiedsectionalflexibilityofacrackedbeam AT lintsanglee modifiedandsimplifiedsectionalflexibilityofacrackedbeam |