  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.
