Control of Snap-Through Transitions in the Response of Mechanically-Equivalent Frequency Modulators

Abstract

Converted energy from ambient loading in civil and mechanical structures is typically used as a viable alternative. Although, piezoelectric vibration harvesters have been widely used given their energy conversion ability, these elements exhibit a narrow natural frequency response range, thus considerably limiting the levels of harvestable power. Recently our group has introduced the concept of using mechanically-equivalent frequency modulators that can transform the low-amplitude and low-rate service and ambient deformations into an amplified input to the piezoelectric transducer. The introduced methods allow energy generation and conversion within the unexplored quasi-static frequency range (≪ 1 Hz). The post-buckling behavior of bilaterally constrained columns was used for frequency up-conversion, and piezoelectric cantilever beams, attached to the columns, were used for energy conversion. The introduced concept was experimentally validated and finite element simulations were developed to evaluate the effect of system parameters (stiffness, thickness, and walls gap) on the position of the snap-through transition events and the levels of force-displacement at the multiple-equilibrium configurations. It was shown that the considered system parameters can determine the absolute levels of force and displacement, but they offer limited control on the number and the relative spacing between the energy-drop events. This paper shows that the combination of multiple slender elastic columns modulators, in parallel configurations, allows for the tailoring of the number and magnitude of the mode branch switching during the postbuckling response of the complete system. Experimental and numerical results are presented to validate the proposed concept.