On some aspects of multiple scale method in problems of nonlinear dynamics

Nonlinear vibrations of the two degree-of-freedom system near resonances are studied. The system is externally and kinematically driven. The dynamical problem is solved by an analytical multiple scales method (MS). This analytical approach gives very good results in solving problems of nonlinear dynamics and is more and more popular in last decades. The investigations are focused on correctness of MS method using various number of considered time scales. Namely, we show that in some cases the use of only two time scales is insufficient to detect all possible resonances exhibited by the studied system.