Exact Model Reduction and Fast Forced Response Calculation in High-Dimensional Nonlinear Mechanical Systems

TL;DR

This paper introduces a spectral submanifold-based method for efficiently computing forced-response curves in high-dimensional nonlinear mechanical systems, eliminating the need for numerical simulation and enabling analysis of larger, more complex models.

Contribution

It presents a novel spectral submanifold approach with multivariate recurrence relations that significantly speeds up forced response calculations in high-dimensional systems.

Findings

Achieves major computational speed-up over previous methods.

Successfully applied to a discretized beam model.

Enables analysis of larger mechanical systems without extensive simulations.

Abstract

We show how spectral submanifold (SSM) theory can be used to extract forced-response curves, including isolas, without any numerical simulation in high-degree-of-freedom, periodically forced mechanical systems. We use multivariate recurrence relations to construct the SSMs, achieving a major speed-up relative to earlier autonomous SSM algorithms. The increase in computational efficiency promises to close the current gap between studying lower-dimensional academic examples and analyzing larger systems obtained from finite-element modeling, as we illustrate on a discretization of a damped-forced beam model.