Bifurcation of nonlinear normal modes in a class of two degree of freedom systems
It is well known that nonlinear forced resonance occurs in the neighborhood of nonlinear normal modes (NNM). Moreover, it was shown that the bifurcations of NNM's affect the topological structure of the resonance curves and the global dynamics. Hence the bifurcation investigation of NNM's is of great practical interest. In this very interesting paper the general class of two degrees of freedom systems with cubic nonlinearities is investigated by a perturbation analysis. The generality of the investigation is possible due to extensive use of computer algebraic methods (MACSYMA). Establishing an approximative first integral, the number and stability of periodic motions is determined. Moreover, the most degenerate bifurcation of periodic motion and a universal unfolding which describes all possible local behavior of periodic motions, is given.
scientific article; zbMATH DE number 482333