Buckling and vibration of slender rings and pipes on an elastic foundation

Resumo

It is well known that thin-walled elastic rings and pipes are prone to buckling instabilities when under
external pressure. A particularly interesting example is the buckling of a thin, elastic ring under hydrostatic
pressure. The buckling load is strongly influenced by the follower force nature of the pressure and, if this effect
is neglected, the prediction of the critical buckling load can be as much as 50% for very thin rings. This work
studies, using a variational nonlinear formulation, the buckling and vibration characteristics of rings and pipes
resting on an elastic Pasternak foundation. First the equation of motion of the pre-loaded ring is derived and the
analytical solution of the eigenvalue problems are obtained. The parametric analysis shows the influence of the
geometric and physical parameters on the critical load, natural frequencies and load-frequency nonlinear relation,
considering the follower force effect of the hydrostatic pressure.