Free vibrations of skirt supported pressure vessels — an engineering application of timoshenko beam theory

Timoshenko beam theory is applied to the study of the free vibrations of skirt supported pressure vessels in this paper; such systems are used in the process and power generation industries as well as aboard nuclear powered vessels. It is shown that the analysis is not significantly more complicated than the analysis of skirt-vessel combinations by Euler-Bernoulli beam theory. This latter analysis is provided in an appendix. Two sets of boundary conditions are considered: namely, the cases of (a) a cantilevered system and (b) a fixed-pinned system. The first two natural frequencies of nine typical cases are calculated and compared with the corresponding results obtained from Euler-Bernoulli beam theory. The numerical differences are significant so that if a beam theory is adequate to model the system, it is clear that Timoshenko beam theory is the appropriate one to use. In addition, the first two mode shapes for a particular case are presented for comparison with the corresponding mode shapes predicted by Euler-Bernoulli beam theory. Finally, some comments on the modeling and analysis of specific, real systems are made. It is emphasized that the purpose of the paper is to demonstrate that Timoshenko beam theory is not unduly difficult to apply to problems of engineering interest when a beam theory model is suitable.