Exact Analytical Solutions for the Free Vibration of Steam Generator U-Tubes

Exact analytical solutions for free vibration of straight tubes have been known for many years, with solutions for curved tubes being developed more recently. In this paper it is shown how these solutions can be exploited to obtain similar solutions for the free vibration of U-tubes. All of the required interface boundary conditions are developed in detail and it is shown how advantage can be taken of U-tube symmetry where it exists. Illustrative results of two studies are presented. This represents, to the author’s knowledge, the first comprehensive analytical study of the U-tube free vibration problem.