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

该项目旨在开发分析、计算和实验工具，用于研究一类特定的晶格网络。本研究特别感兴趣的是局部化和时间周期性的动力学，这可以用于包括振动能量收集在内的各种应用。通过网络的几何形状和连接元素的非线性性质，可以观察到极其丰富的动力学，并通过与工程实验室合作提供的实验数据进行验证。研究结果可用于开发通过环境振动供电的宽带谐振器，其目标是显著减少电池的使用。本项目研究的模型具有二维非线性耦合振荡器的形式，其中耦合由幂律描述。这些方程解的封闭解析表达式是不可用的，因此系统的理论研究将涉及解析近似和数值计算。多尺度方法将用于推导调制方程来描述空间局域化和时间周期解，并将探讨这些近似的误差界限。在参数区域，导出的解析近似是无效的，将采用数值计算。三种情况的例子被考虑为实验实现：颗粒晶体，排斥磁铁和折纸单位细胞。基于磁晶格网络的能量收集概念将被设计、优化、实现和基准测试。

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.