Research Papers

A Modified Fractional Calculus Approach to Model Hysteresis

[+] Author and Article Information
Mohammed Rabius Sunny1

Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061sunny@vt.edu

Rakesh K. Kapania

Mitchell Professor of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061rkapania@vt.edu

Ronald D. Moffitt

 Institute for Advanced Learning and Research, Danville, VA 24540rmoffitt@vt.edu

Amitabh Mishra

Department of Computer Science, Johns Hopkins University, Baltimore, MD 21218amitabh@cs.jhu.edu

Nakhiah Goulbourne

Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061nakg@vt.edu


Corresponding author.

J. Appl. Mech 77(3), 031004 (Feb 01, 2010) (8 pages) doi:10.1115/1.4000413 History: Received July 29, 2008; Revised July 28, 2009; Published February 01, 2010; Online February 01, 2010

This paper describes the development of a fractional calculus approach to model the hysteretic behavior shown by the variation in electrical resistances with strain in conductive polymers. Experiments have been carried out on a conductive polymer nanocomposite sample to study its resistance-strain variation under strain varying with time in a triangular manner. A combined fractional derivative and integer order integral model and a fractional integral model (with two submodels) have been developed to simulate this behavior. The efficiency of these models has been discussed by comparing the results, obtained using these models, with the experimental data. It has been shown that by using only a few parameters, the hysteretic behavior of such materials can be modeled using the fractional calculus with some modifications.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Operator in the Preisach model

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Figure 2

Experimental setup

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Figure 4

Experimental results

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Figure 5

Derivative and integral of order 0.5

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Figure 6

Comparison of results from different models with experimental results



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