Spectral submanifold reduction of high dimensional nonlinear systems for dynamical integrity analysis

Abstract This study leverages spectral submanifold (SSM) theory for model-order reduction to investigate the dynamical integrity of complex engineering systems, specifically, a finite element model of a clamped-clamped von Kármán beam, an experimental water tank with liquid sloshing, a numerical model of a forced pitch-and-plunge airfoil subject to flutter instability, and an axially compressed beam undergoing dynamic buckling. The main objective of this research is to establish an efficient approach for evaluating the dynamical integrity of high-dimensional and experimental systems by exploiting SSM-model reduction techniques. In each case, SSM-based reduced order models are constructed directly from time-series data, leading to reduced systems of minimal dimensionality (2 or 3) that fully capture the most relevant global dynamical phenomena from a qualitative and quantitative viewpoint. This reduction enables the computation of standard dynamical integrity measures with a fraction of the computational cost required by traditional methods. The approach not only validates SSM theory for global dynamics analysis but also highlights its potential as a practical tool for integrating dynamical integrity assessments into engineering design—a step often overlooked in standard practice.