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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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. |
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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 |
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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. |
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School of Mechanical and Aerospace Engineering |
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School of Mechanical and Aerospace Engineering Lin, Rongming Ng, Teng Yong |
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Article |
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Lin, Rongming Ng, Teng Yong |
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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 |
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2020 |
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https://hdl.handle.net/10356/142448 |
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1681056384246874112 |