Stability of an elastic pipe through which a string is pulled with the cons
tant velocity is studied by the Liapunov-Schmidt method. It is assumed that
imperfections in shape (small initial deformation) and loading (distribute
d load along the axis of the pipe) are present. Stability boundary is obtai
ned from the eigenvalues of the linearized equations. It is shown that the
bifurcation is super-critical. The conditions guaranteeing that imperfectio
ns introduced here form a universal unfolding are stated. The post-critical
shape of perfect pipe is determined by numerical integration of the corres
ponding system of equations. For this system of equations we also found two
new first integrals. For the case of Bernoulli-Euler model of the pipe the
post-critical shape is expressed in terms of elliptic integrals. (C) 1999
Elsevier Science Ltd. All rights reserved.