Nonlinear model reduction for a cantilevered pipe conveying fluid: A system with asymmetric damping and stiffness matrices

Abstract

We construct reduced-order models (ROMs) for a geometrically nonlinear viscoelastic cantilevered pipe conveying fluid, a dynamical system that includes asymmetric damping and stiffness matrices and nonlinear internal forces. The asymmetries of the damping and stiffness matrices are resulted from flow-induced gyroscopic and follower forces respectively. The ROMs are constructed using spectral submanifolds (SSMs). Specifically, we use a simulation-free approach implemented in SSMTool, an open-source package that automates the computation of SSMs, to construct the SSM-based ROMs. This approach takes equations of motion of the pipe as inputs and no simulation of the full system is involved. The ROMs enable efficient and accurate predictions of nonlinear dynamics of the system, including free vibration, isolas in forced response curves, bifurcations of periodic and quasi-periodic orbits, and heteroclinic and homoclinic orbits.