Vibrations of cracked functionally graded beams: General solution and application – A review
This paper presents a unified approach to vibration analysis of functionally graded beams with transverse open-edge cracks based on the so-called vibration shape obtained as a general solution of vibration equations in the frequency domain. The crack is modeled by a pair of translational and rotati...
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| Format: | Article |
| Language: | English |
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Publishing House for Science and Technology
2022-12-01
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| Series: | Vietnam Journal of Mechanics |
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| Online Access: | https://vjs.ac.vn/index.php/vjmech/article/view/17986 |
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| author | Nguyen Tien Khiem |
| author_facet | Nguyen Tien Khiem |
| author_sort | Nguyen Tien Khiem |
| collection | DOAJ |
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This paper presents a unified approach to vibration analysis of functionally graded beams with transverse open-edge cracks based on the so-called vibration shape obtained as a general solution of vibration equations in the frequency domain. The crack is modeled by a pair of translational and rotational springs of stiffness computed from the crack depth in dependence upon functionally graded material parameters. The frequency-dependent vibration shape functions allow one not only to obtain the closed-form solution of both free and forced vibrations for multiple cracked FGM beams but also to develop the well-known methods such as Transfer Matrix Method or Dynamic Stiffness Method for analysis of FGM framed structures. The proposed theoretical developments have been illustrated by their application for modal analysis and frequency response analysis of multi-span and multistep beams.
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| format | Article |
| id | doaj-art-58d341a73c8742c29680ee88add00a57 |
| institution | OA Journals |
| issn | 0866-7136 2815-5882 |
| language | English |
| publishDate | 2022-12-01 |
| publisher | Publishing House for Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Mechanics |
| spelling | doaj-art-58d341a73c8742c29680ee88add00a572025-08-20T02:10:38ZengPublishing House for Science and TechnologyVietnam Journal of Mechanics0866-71362815-58822022-12-0144410.15625/0866-7136/17986Vibrations of cracked functionally graded beams: General solution and application – A reviewNguyen Tien Khiem0Vietnam Association for Mechanics (VAM), 264 Doi Can street, Ba Dinh district, Hanoi, Vietnam This paper presents a unified approach to vibration analysis of functionally graded beams with transverse open-edge cracks based on the so-called vibration shape obtained as a general solution of vibration equations in the frequency domain. The crack is modeled by a pair of translational and rotational springs of stiffness computed from the crack depth in dependence upon functionally graded material parameters. The frequency-dependent vibration shape functions allow one not only to obtain the closed-form solution of both free and forced vibrations for multiple cracked FGM beams but also to develop the well-known methods such as Transfer Matrix Method or Dynamic Stiffness Method for analysis of FGM framed structures. The proposed theoretical developments have been illustrated by their application for modal analysis and frequency response analysis of multi-span and multistep beams. https://vjs.ac.vn/index.php/vjmech/article/view/17986functionally graded materialsvibration shape functionsmodal analysisfrequency responsemultiple cracked beams |
| spellingShingle | Nguyen Tien Khiem Vibrations of cracked functionally graded beams: General solution and application – A review Vietnam Journal of Mechanics functionally graded materials vibration shape functions modal analysis frequency response multiple cracked beams |
| title | Vibrations of cracked functionally graded beams: General solution and application – A review |
| title_full | Vibrations of cracked functionally graded beams: General solution and application – A review |
| title_fullStr | Vibrations of cracked functionally graded beams: General solution and application – A review |
| title_full_unstemmed | Vibrations of cracked functionally graded beams: General solution and application – A review |
| title_short | Vibrations of cracked functionally graded beams: General solution and application – A review |
| title_sort | vibrations of cracked functionally graded beams general solution and application a review |
| topic | functionally graded materials vibration shape functions modal analysis frequency response multiple cracked beams |
| url | https://vjs.ac.vn/index.php/vjmech/article/view/17986 |
| work_keys_str_mv | AT nguyentienkhiem vibrationsofcrackedfunctionallygradedbeamsgeneralsolutionandapplicationareview |