Zjawiska rezonansów wewnętrznych w nieliniowych układach drgających

The paper presents a survey of the recent literature on the problems of internal resonances in nonlinear vibrating systems, and gives some new results on the internal resonance of order $\omega_2=3\omega_1$ in a two-degree of-freedom system subjected to harmonic load. Two theoretical methods are used: the Ritz method and the averaging method and results are verified by an analog computer simulation. It is shown that in the neighbourhood of the second principle resonance the two-frequency oscillations occur with the amplitude of the subharmonic of order 1/3 considerably higher than that of the fundamental harmonic component. The Ritz method gives results very close with those of analog computer simulation whereas results obtained by the averaging method are qualitatively different with them. It is also shown that there occurs steady-state almost-periodic response in certain region of the excitation frequency.