Discussion of S. Ponsioen, S, Jain and G. Haller: “Model reduction to spectral submanifolds and forced-response calculation in high-dimensional mechanical systems”, Journal of Sound and Vibration 488, 2020, pages 1–23

Abstract

The authors of the discussed article considered two examples (1) a finite element model of a linear beam with a cubic spring attachment having 10 to 10,000 degrees of freedom, and (2) a finite element model of a geometrically nonlinear Timoshenko beam having 21 degrees of freedom. The authors concluded that Harmonic Balance (HB) becomes intractable for those examples. In this discussion, we falsify this conclusion. We demonstrate that very well-tractable computation effort is obtained when properly using the HB tool NLvib that was also employed in the discussed article. In particular, for (1), the well-known exact condensation to the nonlinear part of the equation system is carried out. For (2), suitable parameters are set for the path continuation and the Newton-type solver. With this, the computation takes from split seconds to about two minutes instead of the many hours reported in the discussed article.