Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response
Abstract
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation results in additional speed-up and better convergence. We show that the solutions of the reformulated equations are in one-to-one correspondence with those of the original integral equations and derive conditions under which a collocation type approximation converges to the exact solution in the reformulated setting. Furthermore, we observe that model reduction using a selected set of vibration modes of the linearized system substantially enhances the computational performance. Finally, we discuss an open-source implementation of this approach and demonstrate the gains in computational performance using three examples that also include nonlinear finite-element models.
Cite
@article{arxiv.2012.00059,
title = {Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response},
author = {Gergely Buza and George Haller and Shobhit Jain},
journal= {arXiv preprint arXiv:2012.00059},
year = {2021}
}