By extending the concept of normal modes of linear vibration systems to non-linear systems,Rosenberg introduced the concept of non-linear normal modes (NNMs).An extension of Rosenbergs definition was introduced by Shaw and Pierce, where the concept of NNMs was defined as two-dimensional invariant manifolds tangent to the hyper-plane spanned by the linear modes in the phase space at the equilibrium points.The knowledge of the modal frequencies of NNMs may provide valuable insight regarding the position of possible resonances, a feature of considerable engineering importance.On the other hand, the mode shapes of NNMs are expected to be used, as their linear counterparts, to efficiently obtain the reduced order model of an original high-dimensional or a continuous engineering system.