Shell Vibration Modes in Thin Wall Pipes Transporting Liquids

Shell mode vibrations in pipes are characterized by their high frequencies relative to those of beam vibration modes. However, for thin walled large diameter pipes, these shell mode frequencies are slightly moderated. The shell mode frequencies are further moderated when the pipes are transporting liquids such as water or molten sodium. In this paper, the inertia of the transported liquid inside the pipe is included in the pipe shell mode frequency formulation. Admissible flow patterns, which satisfy the fluid continuity equation, and compatible with the motion of the pipe shell boundary, are postulated for the shell modes being investigated. Rayleigh’s energy method is used to compare the shell mode frequencies with and without the effects of the liquid inertia. Using water as liquid medium, the frequency of a typical large thin walled pipe is reduced by a factor ranging from 2 to 10. The pipe shell radial-circumferential bending modes are generally characterized by lower frequencies relative to the extension and/or longitudinal shell modes. The inclusion of water as a liquid medium results in further lowering these frequencies by additional 45% to 55%. The frequencies of the pipe shell radial-circumferential bending modes, including water as a liquid medium, could reach the same order of magnitude as those of the piping beam modes. Consequently, the latter are within the seismic cutoff frequency that can not be ignored.