Linear models of dissipation whose Q is almost frequency independent



Laboratory experiments and field observations indicate
that tlie Q of many non ferromagnetic inorganic solids is almost frequency
independent in the range 10' to 10~2 cps; although no single substance has
been investigated over the entire frequency spectrum. One of the purposes
of this investigation is to find the analytic expression of a linear dissipative
mechanism whose Q is almost frequency independent over large frequency
ranges. This will be obtained by introducing fractional derivatives in the
stress strain relation.
Since the aim of this research is to also contribute to elucidating the
dissipating mechanism in the earth free modes, we shall treat the cases of
dissipation in the free purely torsional modes of a shell and the purely
radial vibration of a solid sphere.
The theory is checked with the new values determined for the Q of
the spheroidal free modes of the earth in the range between 10 and 5 minutes
integrated with the Q of the Railegh waves in the range between 5 and 0.6
Another check of the theory is made with the experimental values
of the Q of the longitudinal waves in an alluminimi rod, in the range between
10-5 and 10-3 seconds.
In both clicks the theory represents the observed phenomena very

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Published by INGV, Istituto Nazionale di Geofisica e Vulcanologia - ISSN: 2037-416X