Multiple parametric resonance in a non-linear two degree of freedom system

A non-linear two degrees of freedom dynamical system subjected to parametric excitation is studied. The relationship between the parametric frequency and the natural frequencies of the system are such that the first generalized coordinate is excited into parametric resonance while both generalized coordinates are excited into combination resonance at the same time. The unstable zone and response of the system under multi-resonant condition are then compared with the unstable zones and responses of the system where each type of resonance is treated on an individual basis, assuming the other type of resonance does not occur.