On the comprehensive stability analysis of axially loaded bistable and tristable metastructures

Approaches to systematic analysis of essentially nonlinear structures with multistable responses, controlled buckling and snapping behavior have received much attention recently in the context of mechanical metamaterials design. A snapping bistable element is generally a highly efficient damper, performing well even at very low forcing frequencies. In this paper, we transfer basic tools of the metamaterials analysis to macroscopic systems relevant to civil and mechanical engineering applications. Such systems are comprised of only several bistable elements. Followed by analysis of a single snapping bistable axial (two-force) element, we consider a combination of two elements with antisymmetric properties and demonstrate a robust tristable performance of the resultant structure in low-frequency or quasistatic tension-compression loading cycles. The tristability provides an overall response that is symmetric for tension and compression, which makes it interesting for applications in machinery and large-scale seismic structures.