Predicting Generalized Steady States in Aperiodically Forced Mechanical Systems

TL;DR

This paper develops a systematic method to predict generalized steady states in aperiodically forced nonlinear mechanical systems, outperforming neural networks and direct simulations in speed and accuracy.

Contribution

It introduces a new systematic expansion and numerical algorithm for GSS prediction, eliminating the need for initial convergence and improving efficiency over existing methods.

Findings

The algorithm provides explicit, refinable GSS approximations.

It outperforms neural-network-based predictions in structural dynamics.

GSS computations are faster than direct numerical integration for complex models.

Abstract

The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical algorithm that yields explicit and arbitrarily refinable approximations for GSSs without the need for an initial convergence period. This is to be contrasted with a direct numerical integration of the system, whose convergence is hard to assess or is even undefined for short, transient forcing. When at least the linear part of the equations of motion is known, our GSS algorithm outperforms available data-driven neural-network-based techniques for predicting forced response in structural dynamics problems. In a fully equation-driven setting, our GSS computations are shown to be faster than a direct numerical integration of forced nonlinear finite-element models of beams and shells.