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...

Full description

Saved in:
Bibliographic Details
Main Authors: Lin, Rongming, Ng, Teng Yong
Other Authors: School of Mechanical and Aerospace Engineering
Format: Article
Language:English
Published: 2020
Subjects:
Online Access:https://hdl.handle.net/10356/142448
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
Description
Summary: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.