Stability boundaries of an oscillator under high frequency multicomponent parametric excitation

The method of multiple scales is used to investigate certain of the stability boundaries of a damped single-degree-of-freedom system under a multifrequency parametric excitation having sinusoidal inputs with constant frequency spacing and with initial phase angles. The resonance case studied is that for which the difference between any two excitation frequencies is near to twice the natural frequency. Results obtained are compared with those obtained by the monodromy matrix method which is based on Floquet theory. The results compare closely when the excitation level is small, and agree qualitatively at larger excitation.