Some topics in the free and forced oscillations of a class of nonlinear systems

In this work we examine the free and forced oscillation of a class of two-Degree-of Freedom Undampted Nonlinear Systems. We examine the existence and stability of Similar Normal Modes of the Unsymmetric system and we analyse the subharmonic periodic orbits of the weakly coupled symmetric oscillator. Furthermore, exact solutions for the steady state forced motions of the strongly nonlinear system are derived and specific applications for systems with cubic nonlinearities are given. Finally we give a methodology for examining the Nonsimilar Normal Modes of such systems and we apply the analysis to the case of a weakly coupled system with cubic nonlinearities