RUI: Strongly Nonlinear Dynamics of Lattice Networks: From Analysis to Application

Bowdoin College, Brunswick ME

Investigators

Abstract

This project aims to develop analytical, computational, and experimental tools for the study of a particular class of lattice networks. Of particular interest in this research are the dynamics of localization and time-periodicity, which can be exploited for a variety of applications including vibration energy harvesting. Through the geometry of the network and the nonlinear nature of the connecting elements, extremely rich dynamics can be observed and verified by experimental data provided by collaborations with engineering laboratories. The results could be used to develop broadband resonators that are powered through ambient vibrations, with the goal of significantly reducing battery usage. The models under study in this project have the form of a two-dimensional nonlinear coupled oscillator, where the coupling is described by a power-law. Closed-form analytical expressions for solutions of these equations are not available, and thus the theoretical study of the system will concern analytical approximations and numerical computation. Multiscale methods will be used to derive modulation equations to describe spatially localized and time-periodic solutions, and error bounds for these approximations will be explored. In parametric regions where the derived analytical approximations are not valid, numerical computations will be employed. Three case examples are considered for experimental realizations: granular crystals, repelling magnets, and origami unit cells. An energy harvesting concept based on a magnetic lattice network will be designed, optimized, implemented, and benchmarked.