Model reduction for complex pipes conveying fluid using spectral submanifolds: From circular, S-shaped pipes to pipelines with multiple branches

Abstract

Pipes conveying fluid play a fundamental role in aerospace, nuclear, and civil engineering. Finite element methods, such as the absolute nodal coordinate formulation (ANCF), are powerful tools for modeling complex pipelines that convey fluid. However, the associated finite element models (FEMs) are high-dimensional nonlinear systems, which are computationally expensive to simulate and analyze. Here, we present a model reduction framework for complex pipelines via spectral submanifolds (SSMs) to handle the curse of high dimensionality. We use ANCF to model complex pipelines, derive cubic truncated FEMs of the ANCF-based models to simplify the non-polynomial nonlinearities, and then construct SSM-based reduced-order models (ROMs) for the cubic FEMs. The SSM-based ROMs enable efficient and accurate predictions on the free and forced vibrations of the pipes. We use circular, S-shaped pipes, and a pipeline with multiple branches to demonstrate the effectiveness of the proposed reduction framework. The simulation results demonstrate that the proposed computational framework can accurately capture the intrinsic nonlinear dynamic characteristics while substantially reducing computational cost.