Torsional Vibration of a Hollow Cylinder with Periodic Structure.
STANFORD UNIV CALIF DEPT OF APPLIED MECHANICS
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The theory of torsional vibrations of hollow cylinder, with a periodic structure of elastic constants and density variation normal to the axis of the cylinder is developed in terms of Floquet waves. Floquet waves are quasi-periodic, whose amplitude profile has the same periodicity as that of the material and thus repeats after traveling a complete cell of the cylinder. Using Floquet theory, the dispersion spectrum is obtained for time-harmonic waves propagating normal to the laminations. It is shown that the dispersion spectrum has a banded structure, consisting of passing bands and stopping bands. Some special cases, in which the wave profiles have simple forms are also considered. Also concluded in the analysis is the study of the mode shapes at the two ends of the zone. Author