On the Internal Resonance in a Nonlinear Two-degree-of-freedom System : When the Natural Frequencies Are in the Ratio 2 : 3

Abstract

Forced vibrations of a nonlinear two-degree-of freedom internally-resonanced system with the natural frequencies in the ratio 2:3 are treated. Theoretical analysis is carried out on the behavior of the system near the lower and higher resonance frequencies. The analysis shows that the system can take three different vibratory states depending on the initial condition. In the first state only a harmonic oscillation occurs and this state is similar to the ordinary resonance. In the second state an ultra-subharmonic oscillation of order 3/2 or order 2/3 occurs and in the third, an almost periodic motion occurs. The validity of the theoretical analysis is confirmed by an analog computer.