Buckling and Frequencies of Long Vertical Pipes

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Abstract
The critical lengths (or weights) and the natural frequencies of transverse vibration of vertical pipes having different end constraints are determined by the use of a power series. It is assumed that the pipes are subjected to a hydrostatic pressure. Due to gravity, the axial force in a pipe varies linearly along the length of the pipe. The critical lengths are given in a dimensionless form, and the frequencies are presented numerically as a function of the weight-length parameter. The physical interpretations of the results are also given.

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