Active shaping of a bi-stable potential: Exploring nonlinear coupling to a stiff externally-excited oscillator

The ability to actively shape the potential energy function of a bi-stable oscillator without the use of feedback control offers key advantages in the design of adaptive morphing structures, mechanical switches, vibration absorbers, and energy harvesters. In this paper, we propose an approach based on nonlinearly coupling the bi-stable (low-frequency) oscillator to a stiff (high-frequency) linear oscillator, which, in turn, is excited harmonically near its resonant frequency. We show that active and controlled shaping of the potential energy function can be achieved by changing either the magnitude and/or the frequency of the high-frequency harmonic input. Pronounced shape changes are achieved even for relatively small levels of the input excitation; levels that are much lower than those needed when the bi-stable oscillator is directly subjected to the high-frequency excitation. The study also reveals an interesting phenomenon where the effective potential energy function of the slow dynamics can transition from the bi- to the mono-stable type and vise versa by simply changing the initial conditions of the externally-excited stiff oscillator.