Bifurcations in nonlinear models of fluid-conveying pipes supported at both ends

Stationary bifurcations in several nonlinear models of fluid conveying pipes fixed at both ends are analyzed with the use of Lyapunov–Schmidt reduction and singularity theory. Influence of the gravitational force, curvature and vertical elastic support on various properties of bifurcating solutions are investigated. In particular the conditions for occurrence of supercritical and subcritical bifurcations are presented for the models of Holmes, Thurman and Mote, and Paidoussis.