Local bifurcation analysis of parameter-excited resonance of pipes under thermal load

Abstract

The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is developed according to Hamilton principle. The Galerkin method is adopted to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales and the singularity theory are utilized to analyze the stability and bifurcation of the trivial and non-trivial solutions. The transition sets and bifurcation diagrams are obtained both in the unfolding parameter space and physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and verify the stability and local bifurcation analyses. The critical thermal rates are obtained both by the numerical simulation and the local bifurcation analysis. The natural frequency of lateral vibration decreases as the mean fluid velocity or the thermal rate increases according to the numerical results. The present work can provide valuable information for the design of the pipeline and controllers to prevent structural instability.