山形大学紀要（工学） 第11巻 第1号（1970）55-74
Axisymmetric Vibrations of cylindrical shells with Flanges
Shin TAKAHASHI, Yoshrtaro HIRANO, Katsuyoshi SUZUKI and Shogo TANNO
Vibrational problems of circular cylindrical shells have already been investigated, but research papers on vibrations of thin cylindrical shells with panels or flanges are very few.
The authors investigate axisymmetric vibrations of a cylindrical shell with a concentric circular plate at one end or at each end, respectively.
They obtain the Lagranigan of this combined system by adding the Lagrangian of its circular plates to that of its shell represented by their boundary values respectively, and denote this Lagrangian by the unknown boundary values using the conditions of continuity of its shell and plates.
Then the frequency equations and displacements are given by minimizing the Lagrangian with respect to these unknown boundary values.
There are bending-extensional vibrations and torsional ones in axisymmetric vibrations of this system. Frequencies and displacements for the bending-extensional vibrations are evaluated and shown in graphs in comparison with the results of the cylindrical shells. Vibrations of a cylindrical shell with flanges are much the same as those of a cylindrical shell free at both ends, but in some ranges of the ratio of length to radius, the former frequencies are fairly different from the latter by the influence of the flanges.