Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

TL;DR

This paper presents a method to analytically compute spectral submanifolds and backbone curves from experimental vibration data, enhancing nonlinear model identification for multi-degree-of-freedom mechanical systems.

Contribution

It introduces a novel data-driven approach to determine spectral submanifolds and backbone curves analytically, improving accuracy in nonlinear system modeling.

Findings

Accurately reproduces backbone curves from experimental data.

Demonstrates effectiveness on synthetic and real vibration signals.

Provides a new analytical tool for nonlinear model identification.

Abstract

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.