Semi-analytical solutions for dynamic analysis of fluid conveying pipes by a novel hybrid method

A novel semi-analytical technique termed GFM-Galerkin (a hybrid approach that combines Galerkin method and Green function method) is developed for the dynamic study of fluid conveying pipes. First, the application of GFM to the analytical steady-state displacement response of a Euler-Bernoulli straight beam is reviewed, and then, the closed form mode functions are derived by combining advanced-math with resonance principle. Second, the motion equation of fluid conveying straight pipes is discretized by traditional Galerkin method with unknown shape functions, replacing which by the analytical mode functions deduced in the first step, the specific eigenfunction for flow-induced vibration and the steady-state displacement response for forced vibration are obtained. Finally, several numerical calculations are performed to verify the validity of GFM-Galerkin. A brief description of obtaining in-plane semi-analytical solutions for curved pipes with rigid supports at both ends is also presented, with one example introduced to demonstrate the effectiveness of the proposed technique. The proposed hybrid method broadens the application scopes of the single GFM and Galerkin method by compensating for their limitations in solving dynamic problems. Additionally, it has guiding significance for the development of other hybrid methods for studying fluid solid coupling dynamics or other complex problems in fluid conveying pipes.