  A novel method for the numerical prediction of the slowly varying dynamics of
nonlinear mechanical systems has been developed. The method is restricted to
the regime of an isolated nonlinear mode and consists of a two-step procedure:
In the first step, a multiharmonic analysis of the autonomous system is
performed to directly compute the amplitude-dependent characteristics of the
considered nonlinear mode. In the second step, these modal properties are used
to construct a two-dimensional reduced order model (ROM) that facilitates the
efficient computation of steady-state and unsteady dynamics provided that
nonlinear modal interactions are absent. The proposed methodology is applied to
several nonlinear mechanical systems ranging form single degree-of-freedom to
Finite Element models. Unsteady vibration phenomena such as approaching
behavior towards an equilibrium point or limit cycles, and resonance passages
are studied regarding the effect of various nonlinearities such as cubic
springs, unilateral contact and friction. It is found that the proposed ROM
facilitates very fast and accurate analysis of the slow dynamics of nonlinear
systems. Moreover, the ROM concept offers a huge parameter space including
additional linear damping, stiffness and near-resonant forcing.
