Cusp bifurcation of slightly curved tensioned pipe conveying hot pressurized fluid

In the course of operation of pipes conveying high temperature-high pressure fluid, unexpected behaviors leading to catastrophic failures have been observed. These have been attributed to uncertainties arising from issues not adequately addressed in the design. Sources of such uncertainties include geometric imperfection of the pipe and temperature variation. The perfectly straight pipe is assumed in most designs, but it is an idealization that does not exist in practice. In a bid to reduce the number of uncertainties in design and operation, a model governing nonlinear vibration of tensioned pipes conveying hot pressurized fluid that accounts for the geometric imperfection of the pipe is developed in this work. Coupled nonlinear equations of motion in both axial and transverse directions are obtained and solved using the eigenfunction expansion method. The influence of initial curvature, temperature, and the longitudinal vibration on the pipe are investigated. The results obtained show that a pipe with geometric imperfection exhibits cusp bifurcation and not supercritical pitchfork bifurcation.