Summary
Shallow arches have been used as architectural structures dating back to antiquity. Historically, these structures have been studied under static conditions for their use as load-bearing elements. However, in recent years the dynamic phenomena of the shallow arches, such as snap-through instabilities, have been explored to create multistable mechanical metamaterials (MMM) assembled from arrays of connected shallow arches. Two varieties of shallow arches can be used to assemble such an array: elastically deformed arches (buckled beams) and plastically deformed arches. Using a combination of both types of arches grants additional control of the properties of the MMM such as transition wave speed on non-reciprocity behavior. While the non-linear dynamic behavior of elastically deformed buckled beam has been extensively studied, the plastically deformed arch has not yet been investigated in depth. In this work, we explore the non-linear dynamics of the plastically deformed shallow arch in comparison to its elastic counterpart. Notably, the properties of the plastically deformed arch differ based on which stable configuration the arch is in. As an effect of the asymmetries in the potential energy landscape of the plastically deformed arch, the two stable configurations have different linear equivalent stiffnesses. These differences affect the structure’s natural frequency and non-linear frequency response. This results in the plastically deformed arch capable of changing its properties simply by reconfiguring between stable equilibrium points.
