<p>Fractional calculus is the
integration and differentiation to an arbitrary or fractional order. The
techniques of fractional calculus are not commonly taught in engineering
curricula since physical laws are expressed in integer order notation. Dr.
Richard Magin (2006) notes how engineers occasionally encounter dynamic systems
in which the integer order methods do not properly model the physical
characteristics and lead to numerous mathematical operations. In the following
study, the application of fractional order calculus to approximate the angular
position of the disk oscillating in a Newtonian fluid was experimentally
validated. The proposed experimental study was conducted to model the nonlinear
response of an oscillating system using fractional order calculus. The
integer and fractional order mathematical models solved the differential
equation of motion specific to the experiment. The experimental results were compared to the integer order and
the fractional order analytical solutions. The fractional order
mathematical model in this study approximated the nonlinear response of the
designed system by using the Bagley and Torvik fractional derivative. The
analytical results of the experiment indicate that either the integer or
fractional order methods can be used to approximate the angular position of the
disk oscillating in the homogeneous solution. The following research was in collaboration with Dr. Richard
Mark French, Dr. Garcia Bravo, and Rajarshi Choudhuri, and the experimental
design was derived from the previous experiments conducted in 2018.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12760130 |
| Date | 06 August 2020 |
| Creators | Jordan D.F. Petty (9216107) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Relation | https://figshare.com/articles/thesis/Modeling_a_Dynamic_System_Using_Fractional_Order_Calculus/12760130 |
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