Nonlinear Behaviors of Pipe Conveying Fluid with Retaining Clip in Supercritical Regime

This study explores the nonlinear dynamic behavior of a clamped-clamped pipe conveying fluid and equipped with a retaining clip, subjected to primary resonance under external excitation. The presence of the intermediate clip introduces significant complexity, especially when fluid velocity exceeds the critical threshold. The governing nonlinear equation of motion is derived using Hamilton’s principle and converted via Galerkin’s method into a set of nonlinear ordinary differential equations. These equations are then analyzed using the method of multiple scales. The analysis focuses on the supercritical flow regime and investigates frequency and force response characteristics. Internal resonance at a 2:1 ratio is studied across varying clip stiffness levels. Furthermore, the impact of clip stiffness, damping coefficient, and detuning parameters on Hopf bifurcation, saddle-node behavior, and system responses is examined. This study reveals that increasing clip stiffness elevates critical velocities and induces complex dynamics, including internal resonance and transitions to multiperiodic and quasiperiodic behaviors. The findings underscore the need for precise tuning of stiffness and damping to ensure system stability and avoid undesired responses.