The Fractional Derivative as a Complex Eigenvalue Problem

  • Masaharu Kuroda
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 30)

Abstract

For the dynamics described by an equation of motion including fractional-order-derivative terms, the fractional-order-derivative responses cannot be measured directly through experiments. In the present study, three solutions are proposed that enable the fractional-order-derivative responses to be measured by a combination of signals obtained by existing sensors. Specialized sensors or complicated signal processing are not necessary. Fractional-order-derivative responses at a certain point on a structure can be expressed through linear combinations of the displacement signal and the velocity signal at each point on the structure. Although their calculation processes are different, all three methods eventually reach the same result.

Keywords

Fractional Derivative Mass Point Fractional Calculus System Matrix Fractional Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Dordrecht Heidelberg London New York 2011

Authors and Affiliations

  • Masaharu Kuroda
    • 1
  1. 1.National Institute of Advanced Industrial Science and Technology (AIST)TsukubaJapan

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