Buckling and Frequencies of Long Vertical Pipes

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.