A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

Abstract

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. 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 mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

The Influence of Rotation on Vibration of a Thick Cylindrical Shell

“…From Table 1, it is observed that a good agreement between the present calculated results and the results of literature [25] has been obtained.…”

“…The boundary conditions are free at both ends ( Figure 1). The cylindrical shell has the following geometric properties and material properties, which are the same as that used in reference [25]. The only di!erence is that this is a rotating cylindrical shell now: l"0)254 m, r"0)09525 m, t"0)0381 m, E"2)07;10 N/m, "0)28, "7)86;10 kg/m.…”

“…In order to verify the program, we have calculated the stationary cylinder to compare with the results of Wang [25]. The comparison results are presented in Table 1.…”

“…The modes of stationary thick cylinders were classi"ed into eight categories by Wang and Williams [25]. However, no work on the three-dimensional mode shapes of a thick rotating cylinder has been carried out.…”

“…It is clearly impossible for several frequencies to have exactly the same mode shape. Recently, Wang and Williams [25] proposed a di!erent mode classi"cation of "nite-length thick cylinders, based on their three-dimensional mode shapes. Using this classi"cation together with the descriptors n and m, all of the vibrational modes of "nite-length thick cylinders can be identi"ed uniquely.…”