Switching from primary to subharmonic resonances in nonlinear systems

This work proposes a simple method to switch between the primary and subharmonic resonances of nonlinear systems. For a primary resonance harmonically excited at a specific forcing amplitude, there exists another forcing amplitude at an integer multiple
of the fundamental frequency allowing for the excitation of the corresponding subharmonic resonance having the same amplitude and frequency. Using an energy analysis, it is possible to determine the necessary forcing amplitude change to switch to the targeted subharmonic resonance. The proposed method is numerically illustrated with a transition from a 1:1 to a 1:3 resonance of a Duffing oscillator.