Linear models of dissipation whose Q is almost frequency independent
Abstrak
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 minutes. 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 satisfactory.
Topik & Kata Kunci
Penulis (1)
M. Caputo
Akses Cepat
- Tahun Terbit
- 1966
- Bahasa
- en
- Total Sitasi
- 865×
- Sumber Database
- Semantic Scholar
- DOI
- 10.4401/AG-5051
- Akses
- Open Access ✓