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Energy Considerations for Fractional Elements

[+] Author Affiliations
Carl F. Lorenzo

NASA Glenn Research Center, Cleveland, OH

Tom T. Hartley

University of Akron, Akron, OH

Paper No. DETC2013-13247, pp. V004T08A029; 7 pages
doi:10.1115/DETC2013-13247
From:
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5591-1
  • Copyright © 2013 by ASME

abstract

This paper considers the energy aspects of fractional elements defined by the equation Display FormulaFt=kλDtλ0xt. In contrast to the typically conservative assumption of classical physics that lead to the potential and kinetic energy expressions, a number of important non-conservative differences are exposed. Firstly, the considerations must be time-based rather than displacement or momentum based variables. Time based equations for energy behavior of fractional elements are presented and example applications are considered. The effect of fractional order on the energy requirements and energy return of these systems is shown. Importantly, it is shown that the history, or initialization, has a strong effect on energy requirements. Finally, compact expressions for the work or energy, are developed.

Copyright © 2013 by ASME

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