Integral equations and model reduction for fast computation of nonlinear periodic response. (24th May 2021)

• Record Type: Journal Article
• Authors: Buza, Gergely; Haller, George; Jain, Shobhit
• Is Part Of: International journal for numerical methods in engineering. Volume 122:Number 17(2021)
• Page Start: 4637
• Page End: 4659
• Publication Date: 2021-05-24
• Subjects: integral equations -- model order reduction -- nonlinear oscillations -- periodic response -- structural dynamics; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6740
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: We propose a reformulation for a recent integral equations approach 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.