A Gegenbauer-polynomial-based semi-analytical approach for dynamic modeling of series-parallel pipe systems under elastic boundary conditions

This study introduces a Gegenbauer-polynomial-based semi-analytical approach (GP-SAA) for dynamic modeling of series-parallel pipe (SPP) systems under elastic boundary conditions. By leveraging the Timoshenko beam theory, energy formulations for straight and curved pipes, single and dual clamps, and pipe joints are derived. The Virtual Spring Technology (VST), which effectively models the dynamic coupling effects arising from pipe-pipe, clamp-pipe, and pipe-connector interactions, is employed to establish elastic boundary conditions. To ensure the numerical accuracy and computational efficiency of the GP-SAA framework, a systematic convergence analysis of key parameters is performed. A prototype of the SPP system and its finite element (FE) model are independently developed to benchmark the proposed methodology via the experimental modal analysis. Convergence studies based on multiple realizations of the polynomial parameter are conducted to identify a proper truncation term for the GP-SAA. Furthermore, parametric investigations into critical factors such as pipe geometry, clamp positions, and connector locations are performed to investigate their combined effects on natural frequency characteristics of the SPP system. Numerical results demonstrate the effectiveness and potential applicability of the GP-SAA for dynamic modeling of SPP systems in general.