Constrained-Energy Dynamic Cross-Well Motion of Bistable Structures Subjected to Noise Disturbance

Abstract

Bistable structures have two stable equilibrium positions and can be utilized to maintain a static shape with no energy consumption. This paper focuses on the minimum energy required for performing snap-through of a bistable structure subjected to noise disturbance. This paper uses the Duffing–Holmes equation as a one-degree-of-freedom representative model of a bistable structure. This equation is numerically solved to calculate the energy required for cross-well oscillation under different system and forcing conditions. The paper shows how the energy required for cross-well transfer varies as a function of damping ratio and frequency ratio at specific harmonic force amplitude when the system is externally disturbed with a band-limited noise signal. A magneto-elastic bistable beam is fabricated and tested to validate the used mathematical model. Various nondimensional parameters are used to highlight interesting phenomena. The relationships between signal-to-noise ratio (SNR), dynamic-to-static force ratio, and damping ratio to the response behavior are shown. It is found that the domain of low energy regions decreases by increasing the level of noise. Additionally, underactuated bistable and linear systems behave similarly for high levels of noise. This paper specifically identifies the critical force ratio, which allows for snap-through as a function of critical nondimensional system parameters.