The theory of vibrations in cylindrical pipes within the context of thin shell theory is reviewed. Beginning with a summary of the thin shell equations of motion and their application to cylindrical shells, solutions are obtained for a specific example of a typical pipe for each of several thin shell theories including: Donnell's theory, Love's theory and an improved theory which includes the effects of rotary inertia and transverse shear. For comparison, finite element (FE) models of the pipe are also constructed. To investigate the effect of shell curvature on the thin shell equations, various models of open shells evolving from a curved plate are also examined. The FE results are shown to agree well with those from the improved theory over the range of frequencies studied (the lowest 15–20 modes), though the time for their computation when using commercial FE software is three orders of magnitude longer
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