On vibration control using a bistable snap through absorber from a force balance perspective

One approach to vibration control is to apply a force to a primary structure which opposes excitation, effectively canceling the external disturbance. A familiar passive example of this approach is the linear tuned mass absorber. In this spirit, the utility of a bistable attachment for attenuating vibrations, especially in terms of the high-orbit, snap through dynamic, is investigated using the harmonic balance method and experiments. Analyses demonstrate the fundamental harmonic snap through dynamic, having commensurate frequency with the single-frequency harmonic excitation, may yield displacements either substantially in-phase or out-of-phase with the primary structure. During in-phase snap through, forces are generated by the bistable oscillator which reinforce the applied loading, resulting in dramatic amplification of primary system response. During out-of-phase snap through, forces are generated which are only partially opposed to the input, leading to a measure of host structure attenuation. The experiments verify the analytical findings and also uncover nonlinear dynamics not predicted by the analysis that have slightly favorable vibration suppression performance when compared with the out-of-phase, fundamental harmonic snap through action.