On Nonlinear Normal Modes of Systems With Internal Resonance

摘要: A complex-variable invariant-manifold approach is used to construct the normal modes of weakly nonlinear discrete systems with cubic geometric nonlinearities and either a one-to-one or three-to-one internal resonance. The mode shapes are assumed be slightly curved four-dimensional manifolds tangent linear eigenspaces two involved in resonance at equilibrium position. dynamics on these governed by three first-order autonomous equations. In contrast case no resonance, number may more than modes. Bifrcations calculated investigated.