  Frequency responses of multi-degree-of-freedom mechanical systems with weak
forcing and damping can be studied as perturbations from their conservative
limit. Specifically, recent results show how bifurcations near resonances can
be predicted analytically from conservative families of periodic orbits
(nonlinear normal modes). However, the stability of forced-damped motions is
generally determined a posteriori via numerical simulations. In this paper, we
present analytic results on the stability of periodic orbits that perturb from
conservative nonlinear normal modes. In contrast with prior approaches to the
same problem, our method can tackle strongly nonlinear oscillations, high-order
resonances and arbitrary types of non-conservative forces affecting the system,
as we show with specific examples.
