Effects of High Frequency Horizontal Base Excitation on a Bistable System

High frequency excitation (HFE) is known to induce various nontrivial effects, such as system stiffening, biasing, and the smoothing of discontinuities in dynamical systems. These effects become increasingly pertinent in multistable systems, where the system's bias toward a certain equilibrium state can depend heavily on the combination of forcing parameters, leading to stability in some scenarios and instability in others. In this initial investigation, our objective is to pinpoint the specific parameter ranges in which the bistable system demonstrates typical HFE effects, both through numerical simulations and experimental observations. To accomplish this, we utilize the method of multiple scales to analyze the interplay among different time scales. The equation of slow dynamics reveals how the excitation parameters lead to a change in stability of equilibrium points. Additionally, we delineate the parameter ranges where stabilizing previously unstable equilibrium configurations is achievable. We demonstrate the typical positional biasing effect of high-frequency excitation that leads to a shift in the equilibrium points as the excitation parameter is varied. This kind of excitation can enable the active shaping of potential wells. Finally, we qualitatively validate our numerical findings through experimental testing using a simplistic model made with LEGOs.