Nonlinear analysis of forced mechanical systemswith internal resonance using spectral submanifolds, Part I: Periodic response and forced response curve

Abstract We show how spectral submanifold theory can be used to construct reduced-order models for harmonically excited mechanical systems with internal resonances. Efficient calculations of periodic and quasi-periodic responses the are discussed in this paper its companion, Part II, respectively. The dimension a model is determined by number modes involved resonance, independently full system. system obtained as equilibria on submanifolds. forced response curve orbits then becomes manifold equilibria, which easily extracted using parameter continuation. To demonstrate effectiveness efficiency reduction, we compute curves several high-dimensional nonlinear systems, including finite-element von Kármán beam plate.