Nonlinear normal modes in damped forced systems

Abstract

In the previous chapters of this volume, the nonlinear normal modes (NNMs) were defined and explored in conservative systems. In current chapter, the notion is extended for dynamical systems with viscous damping, as well as for the systems with external forcing. We start with a discussion about normal modes in linear damped systems. Then, we discuss an effect of the damping on the NNMs in nonlinear models. Finally, it is demonstrated that the problem of targeted energy transfer (TET) may be efficiently treated with the help of the NNM concept with account of possible time scale separation – both in autonomous and in forced systems.