Non-smooth dynamics of buckling based metainterfaces: rocking-like motion and bifurcations

TL;DR

This paper explores the complex non-smooth dynamics of buckling-based metainterfaces, revealing bifurcations, multistability, and chaotic responses, with implications for designing vibration and energy harvesting devices.

Contribution

It introduces a novel theoretical framework linking buckling dynamics to rocking motion, analyzing bifurcations and multistability in a reduced single-degree-of-freedom model.

Findings

Identification of various bifurcations including period doubling and grazing.

Discovery of broad multistability extending to monostable conditions.

Potential applications in vibration control and energy harvesting devices.

Abstract

The non-smooth dynamics is investigated for an elastic planar metainterface composed by two layers of buckling elements, each one allowing motion on one side only. Through the analogy between buckling and unilateral contact and by assuming no-bouncing at impact, the motion of the relevant two degrees of freedom system is reduced to that of a single degree governed by a piecewise-smooth differential equation. The metainterface dynamics has strong similarities with the rocking motion of rigid blocks and displays several types of dynamic bifurcations in the presence of oscillatory forces, including period doubling, branch point cycle, grazing, as well as quasi-periodic and chaotic responses. Moreover, the multistable response is found to be broaden to conditions representative of monostable states within a quasi-static setting, disclosing a multistability anticipation by dynamics. The wide landscape of the dynamic response for the buckling based metainterface provides a novel theoretical framework to be exploited in the design of mechanical devices for vibration attenuation and for energy harvesting.