Free vibration of circular cylinders of variable thickness

Flexural vibrations of finite length circular cylinders with shear diaphragm ends and symmetric circumferential wall thickness variations are described by using the Rayleigh-Ritz method. Both symmetric and asymmetric solutions are presented. Only circumferential variations in the wall radial dimension are considered; the method is amenable, however, to consideration of longitudinal variations in wall thickness as well. The cylinder wall thickness variation is described as a Fourier series and the vibration is described as a series of modes of a uniform cylinder with the same mean radius. The theory has been applied to a cylinder whose inner bore is circular but is non-concentric with the circular outer surface. The mode shapes have been investigated experimentally by using time-averaged holograms of the vibrating cylinder and the results compare well with the predictions of the theory. The frequencies of the modes agree with the theoretical predictions to within 2%.