Theory and experiment on establishing the stability boundaries of a one-degree-of-freedom system under two high-frequency parametric excitation inputs

The stability of a single-degree-of-freedom linear system to two high-frequency parametric inputs is considered. Equations defining approximately the stability boundaries of the system are developed using Strubleʹs method. The results of the analysis for a range of input frequency ratios and input amplitudes are compared with exact solutions for the regions of instability calculated from the monodromy matrix. Good agreement is found for low excitation levels. Experimental work involving the small amplitude oscillation of a pendulum under two frequency parametric motion is described, instability zones are found to exist and their stability boundaries shown to be reasonably close to those derived from the theory.