We have reproduced our disputed simulation results from our original article as well as the simulations of the discussion article of Krack and Gross referenced above in the title. We have found several inaccuracies and omissions in the discussion article that invalidate its authors’ main claims. We also briefly address inherent performance differences between the SSMTool and the NLvib algorithms to the benefit of the former.

We show how spectral submanifold (SSM) theory can be used to extract forced-response curves 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 two different discretized damped-forced beam models. Using the exact reduction procedure via SSMs for obtaining forced response curves, we further demonstrate speed gains of several orders in magnitude relative to the available state-of-the-art continuation packages, while retaining accuracy.