English

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

Dynamical Systems 2019-12-25 v1

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.

Keywords

Cite

@article{arxiv.1912.11399,
  title  = {Exact Model Reduction and Fast Forced Response Calculation in High-Dimensional Nonlinear Mechanical Systems},
  author = {Sten Ponsioen and George Haller},
  journal= {arXiv preprint arXiv:1912.11399},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1812.06664

R2 v1 2026-06-23T12:55:48.757Z