Dynamics of topological metastructures: nonlinearities and quasi-periodicity (Conference Presentation)

Abstract

Topology has recently emerged as a principle governing unique wave transport phenomena through interface or edge modes that are impurity-immune and potentially unidirectional. In mechanics, these phenomena arise by marrying the notion of material and structure, and are expected to lead to functionalities at the mesoscale that are unattainable solely based on the properties of constituents. Beyond the mere notion of a material, these meta-structures draw their unique characteristics from their finite size and the existence of interfaces. The resulting structural assemblies are expected to feature unprecedented performance in terms of stress wave mitigation, wave guiding, acoustic absorption, and vibration isolation. The seminar illustrates investigations on the effects of nonlinearities on topological properties, and the study of quasi-periodic assemblies. Investigation of the effects of nonlinearities on topological properties allows the exploration of the appearance/robustness of edge and localized modes in the presence of nonlinearities. In addition, the study of lattices with quasi-periodic configurations uncover additional unique properties related to vibration localization in one-dimensional and two-dimensional systems. These can be as interesting if not more useful than the interface modes that are found in periodic structures, as the quasi-periodicity framework provides a consistent methodology that leads to vibration confinement in systems that are not ordered, but are described by deterministic property distributions. Beam and plate structures with quasiperiodic arrangements of grounding springs and lumped masses are presented as structural components which support a variety of localized modes and that are suitable for the experimental characterization of the dynamic behavior of these configurations.