IngentaConnect VIBRATIONAL MODES OF THICK CYLINDERS OF FINITE LENGTH

Abstract:

The natural frequencies and mode shapes of finite length thick cylinders are of considerable engineering importance. A comprehensive classification of the modes of such thick cylinders, based on three-dimentional mode shapes, is presented in this paper. In addition to the 5 groups consisting of pure radial, radial motion with radial shearing, extensional, axial bending, and global modes, as previously adopted for thin cylinders, a futher sixth circumferential category is proposed. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The classification for the modes of thick cylinders is applied to four groups of cylinder whose radial thickness to median radius ratio varies from 0?1 to 0?4. Each group contains a set of 8 cylinders with similar inside and outside diameters, but with different axial lengths; these were used to verify the validity of the classifications, and to study the effects of varying axial length and varying radial thickness on each of the different types of modes. Analytical finite element analysis was applied to all four groups, and experimental anlysis was applied to those cylinders whose radial thickness to the medium radius ratio was 0?4. The results support the method of classification, although very short cylinders behave essentially as annular circular plates. The effects of varying axial length and radial thickness on the vibrational modes are such that all modes can be broadly categorized as either pure radial modes, or non-pure radial modes. The natural frequencies of the former are dependent upon only the radial dimensions of the models, while the natural frequencies of the latter are dependent upon both axial length and radial thickness.

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