Principal trajectories of forced vibrations for discrete and continuous systems

Principal trajectories of forced vibration of linear and nonlinear continuo us systems are introduced as such motions in which the system is equivalent to a Newtonian particle in the function space of the system configurations . The corresponding 'effective mass' of the particle gives physical charact eristics of the system response, so that zero effective mass is associated with resonance. The methodology can be viewed as a complementary tool to th e method of normal modes, when considering the class of forced vibrating sy stems, since the related basis accounts for the system physical properties as well as the external forcing factor. In particular, it is shown that a t wo degrees of freedom system can possess an infinite discrete set of in-pha se and out-of-phase forced vibrations of the normal modes type. The corresp onding forcing vector-functions obey the second Newton law due to the defin ition of principal trajectories.