Executive Summary : | The recent advances in Topological Mechanical Metamaterials have shown novel ways of manipulating energy propagation in materials robustly. This robustness stems from the intrinsic band topology of these systems. Understanding of this phenomenon in materials has not only become important due to its fundamental profoundness, but also, because it may lead to a new class of efficient materials for future sensing, vibration isolation, crashworthiness, and energy harvesting. Topological Mechanical Metamaterials designed so far mostly rely on the linear dynamics of the system. One of the challenging questions in the area is whether topological robustness can be defined in a nonlinear system as well. Moreover, how nonlinearity can be used as a tuning knob to manipulate the topological properties of such metamaterials is largely unknown. Therefore, the objective of this project is to investigate the interplay of topology and nonlinearity in mechanical systems. The project will build on known Topological Mechanical Metamaterials and study the role of nonlinearity on the nontrivial states of the system. In the first part of the project, the dynamics of low-dimensional nonlinear lattices will be thoroughly investigated analytically and numerically. In the second part of the project, theoretical predictions will be validated by vibration experiments on carefully designed (3D printed) structures. Given the design freedom that mechanical systems offer, various types of geometric nonlinearities can be designed in mechanical metamaterials. Due to this versatile nature, the outcome of this research will give a significant push in our understanding of nonlinearity in Topological Metamaterials, relevant to not only mechanics, but also, photonics, ultracold atoms, and electronic circuits. The outcome of this research will also pave the way for designing novel mechanical structures for manipulating large-amplitude waves and vibrations, as encountered in several engineering applications. |