Data-Driven Reduction of the Finite-Element Model of a Tribomechadynamics Benchmark Problem

TL;DR

This paper develops a data-driven reduced-order model for a complex, high-dimensional FEM of a tribomechadynamics benchmark with bolted joints, enabling efficient and accurate nonlinear dynamic predictions.

Contribution

It introduces a spectral submanifold-based approach to create a smooth, low-dimensional model from limited transient data of a large FEM with nonlinear contact and friction.

Findings

The reduced model has 4 dimensions.

It accurately predicts nonlinear forced responses.

It significantly reduces computational cost.

Abstract

Bolted joints can exhibit nonsmooth and significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric nonlinearity. Owing to the nonlinearity and high dimensionality of such models, full-order dynamic simulations are computationally expensive. In this work, we use the theory of Spectral Submanifolds (SSMs) to construct a data-driven, smoothed reduced model for a 187,920-dimensional FEM model of a broadly studied Tribomechadynamics benchmark structure with bolted joints. We train the 4-dimensional reduced model using only a few transient trajectories of the full unforced FEM model. We show that this smooth model accurately predicts the experimentally observed nonlinear forced response of the full nonsmooth benchmark problem.