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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Main Author: Nguyen Tien Khiem
Format: Article
Language:English
Published: Publishing House for Science and Technology 2022-12-01
Series:Vietnam Journal of Mechanics
Subjects:
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
description 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.
format Article
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institution OA Journals
issn 0866-7136
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publishDate 2022-12-01
publisher Publishing House for Science and Technology
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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