FREE-VIBRATIONS OF THICK HOLLOW CIRCULAR-CYLINDERS FROM 3-DIMENSIONALANALYSIS

A three-dimensional (3-D) method of analysis is developed for the free vibration frequencies of hollow circular cylinders of elastic materia l. The method is based upon local coordinates whose origin is attached to the center of cylindrical wall. It assumes for the three displacem ent components a Fourier series in the circumferential (theta) directi on and algebraic polynomials in the radial (q) and axial (z) direction s. Convergence studies for completely free cylinders show that the ana lysis can yield frequencies which are exact to five or six significant figures. These accurate frequencies are compared with those from othe r 3-D analyses available for free hollow circular cylinders having var ious length-to-outside diameter (L/D-o) and inside-to-outside diameter (D-i/D-o) ratios. Extensive, accurate data are presented for the firs t 10 frequencies of each circumferential wave number 0 through 5 for h ollow circular cylinders having D-i/D-o of 0.1, 0.5, and 0.9, with L/D -o = 0.2, 1 and 5 and a Poisson's ratio (nu) = 0.3.