Abstract
Stability of an elastic pipe through which a string is pulled with the constant velocity is studied by the Liapunov– Schmidt method. It is assumed that imperfections in shape (small initial deformation) and loading (distributed load along the axis of the pipe) are present. Stability boundary is obtained from the eigenvalues of the linearized equations. It is shown that the bifurcation is super-critical. The conditions guaranteeing that imperfections introduced here form a universal unfolding are stated. The post-critical shape of perfect pipe is determined by numerical integration of the corresponding 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.
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