Internal resonance and stress distribution of pipes conveying fluid in supercritical regime

Internal resonance and stress distribution of pipes conveying fluid at the supercritical flow around curves have been firstly investigated, with the goal of improving the mechanical fatigue properties of such pipes. Axial pre-pressure as a way of regulating the onset and growth of 1:3 internal resonance has been examined. Based on the direct multi-scale method and the Galerkin method, an approach has been proposed to analyze the nonlinear gyroscopic elastic system with time-dependent nonlinear perturbations. The tensile, bending, and resultant vibratory stress distributions of the pipe system have been determined in the presence of 1:3 internal resonance. Internal resonance degrading fatigue properties of the pipes has been highlighted. The numerical simulations support the analytical results. Then the analytical frequency responses are employed to identify factors that govern the internal resonance and stress distribution and to offer explanations as to why improving fatigue life is accompanied by suppression in the internal resonance. The boundary for incurring internal resonance suggests that appropriate axial pre-pressure should be modified in the presence of 1:3 internal resonance at different fluid velocities.