Coupled vibration of isotropic metal hollow cylinders with large geometrical dimensions

In this paper, the coupled vibration of isotropic metal hollow cylinders with large geometrical dimensions is studied by using an approximate analytic method. According to this method, when the equivalent mechanical coupling coefficient that is defined as the stress ratio is introduced, the coupled vibration of a metal hollow cylinder is reduced to two equivalent one-dimensional vibrations, one is an equivalent longitudinal extensional vibration in the height direction of the cylinder, and the other is an equivalent plane radial vibration in the radius direction. These two equivalent vibrations are coupled to each other by the equivalent mechanical coupling coefficient. The resonance frequency equation of metal hollow cylinders in coupled vibration is derived and longitudinal and radial resonance frequencies are computed. For comparison, the resonance frequencies of the hollow cylinders are also computed by using numerical method. The analysis shows that the results from these two methods are in a good agreement with each other.