Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, June 7, 1999; final revision, Apr. 24, 2000. Associate Editor: A. A. Ferri.

All dynamic systems exhibit some degree of internal damping. Recent investigations have shown that a fractional derivative model provides a better representation of the internal damping of a material than an ordinary derivative model does. For a survey of fractional damping models and their applications to engineering systems, the readers are referred to Rossikhin and Shitikova 1 and the references therein. Traditionally, the Newton’s law is used to model such nonconservative systems, and when a Lagrangian, Hamiltonian, variational, or other energy-based approach is used, it is modified so that the resulting equations match those obtained using the Newtonian’s approach.

Several attempts have been made to include...

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