Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives

Fractional derivative is increasingly being deployed to improve existing mathematical models due to its unique capability in describing anomalous behavior and memory effects which are common characteristics of natural phenomena. Improved vibration analysis has been accomplished by introducing fracti...

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Main Authors: Lin, Rongming, Ng, Teng Yong
Other Authors: School of Mechanical and Aerospace Engineering
Format: Article
Language:English
Published: 2020
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Online Access:https://hdl.handle.net/10356/142448
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1424482020-06-22T06:30:06Z Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives Lin, Rongming Ng, Teng Yong School of Mechanical and Aerospace Engineering Engineering::Mechanical engineering Fractional Derivative Iterative Eigensolution Method Fractional derivative is increasingly being deployed to improve existing mathematical models due to its unique capability in describing anomalous behavior and memory effects which are common characteristics of natural phenomena. Improved vibration analysis has been accomplished by introducing fractional derivatives to model viscoelastic damping and vibration propagation through complex media and much research has been carried out to date. However, much of these existing research efforts have been sporadic to the best and there remains a pressing need to develop a consistent and systematic theoretical framework for vibration analysis of fractional systems to synergize for more productive and coordinated efforts in the area. This paper seeks to address some fundamental issues to facilitate further development such as the definition of general form of a fractional vibration system, its eigenvalue problem and methods of solution, definition of frequency response functions and applicability of conventional modal analysis, equivalent eigensystem and its more efficient eigensolution. With these important issues being resolved to clear the myth, vibration studies of fractional systems can be encouraged and expected to grow in a more fruitful direction. New methods developed and concepts discussed in the paper have all been validated through realistic numerical case studies based on a practical GARTEUR structure with viscoelastic supports modeled using fractional derivatives. 2020-06-22T06:30:06Z 2020-06-22T06:30:06Z 2018 Journal Article Lin, R., & Ng, T. Y. (2019). Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives. Mechanical Systems and Signal Processing, 116, 78-96. doi:10.1016/j.ymssp.2018.06.020 0888-3270 https://hdl.handle.net/10356/142448 10.1016/j.ymssp.2018.06.020 2-s2.0-85049336531 116 78 96 en Mechanical Systems and Signal Processing © 2018 Elsevier Ltd. All rights reserved.
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic Engineering::Mechanical engineering
Fractional Derivative
Iterative Eigensolution Method
spellingShingle Engineering::Mechanical engineering
Fractional Derivative
Iterative Eigensolution Method
Lin, Rongming
Ng, Teng Yong
Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives
description Fractional derivative is increasingly being deployed to improve existing mathematical models due to its unique capability in describing anomalous behavior and memory effects which are common characteristics of natural phenomena. Improved vibration analysis has been accomplished by introducing fractional derivatives to model viscoelastic damping and vibration propagation through complex media and much research has been carried out to date. However, much of these existing research efforts have been sporadic to the best and there remains a pressing need to develop a consistent and systematic theoretical framework for vibration analysis of fractional systems to synergize for more productive and coordinated efforts in the area. This paper seeks to address some fundamental issues to facilitate further development such as the definition of general form of a fractional vibration system, its eigenvalue problem and methods of solution, definition of frequency response functions and applicability of conventional modal analysis, equivalent eigensystem and its more efficient eigensolution. With these important issues being resolved to clear the myth, vibration studies of fractional systems can be encouraged and expected to grow in a more fruitful direction. New methods developed and concepts discussed in the paper have all been validated through realistic numerical case studies based on a practical GARTEUR structure with viscoelastic supports modeled using fractional derivatives.
author2 School of Mechanical and Aerospace Engineering
author_facet School of Mechanical and Aerospace Engineering
Lin, Rongming
Ng, Teng Yong
format Article
author Lin, Rongming
Ng, Teng Yong
author_sort Lin, Rongming
title Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives
title_short Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives
title_full Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives
title_fullStr Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives
title_full_unstemmed Development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives
title_sort development of a theoretical framework for vibration analysis of the class of problems described by fractional derivatives
publishDate 2020
url https://hdl.handle.net/10356/142448
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