Non-intrusive spectral submanifold model reduction for geometrically nonlinear rotating structures with Coriolis and centrifugal forces

TL;DR

This paper introduces a non-intrusive spectral submanifold (SSM) model reduction technique for finite element models of rotating structures, enabling efficient and accurate nonlinear vibration analysis considering geometric nonlinearity, Coriolis, and centrifugal effects.

Contribution

The authors develop a non-intrusive SSM-based reduced-order modeling approach for FE models of rotating structures, verified with COMSOL simulations, capturing complex nonlinear dynamics efficiently.

Findings

SSM-based ROM accurately predicts backbone and forced response curves.

Coriolis force significantly influences nonlinear vibration behavior.

Method validated on various rotating structure examples.

Abstract

Rotating structures are widely observed in engineering applications such as turbomachinary and wind turbine. These rotating structures, particularly for blades made by lightweight materials, can undergo large deformation in operations and display complex nonlinear dynamics under the coupling interaction of geometric nonlinearity, Coriolis effect and centrifugal force. Finite element (FE) methods provide a powerful and accurate modeling approach for capturing the complex nonlinear dynamics for realistic rotating structures, yet its high-dimensionality causes significant challenge to efficient prediction for the nonlinear vibration. Here, we present a non-intrusive spectral submanifold (SSM) model reduction for these FE models of rotating structures. We use COMSOL to establish FE models and simulate these FE models to verify the accuracy of SSM-based reduction. We first compute nontrivial static equilibrium induced by the centrifugal force and then construct non-intrusively SSM based reduced-order model (ROM) anchored at the equilibrium. These SSM-based ROMs enable efficient and accurate extraction of backbone and forced response curves. We use a suite of examples with increasing complexity to demonstrate the effectiveness of the SSM reduction, including a rotating beam, a twisted plate, a rotor with two disks, and an internally resonant fan with three blades. The obtained results also highlight the significant effects of Coriolis force on the nonlinear vibration of rotating structures.