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

RUI：格子网络的强非线性动力学：从分析到应用

• 批准号: 1615037
• 负责人: Christopher Chong
• 金额: $ 9.86万
• 依托单位: Bowdoin College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1615037&HistoricalAwards=false
• 关键词: RUI; Strongly; Nonlinear; Dynamics; Lattice

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.

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格型网络。在这项研究中特别感兴趣的是本地化和时间周期性的动态，这可以被利用为各种应用，包括振动能量收集。通过网络的几何形状和连接元件的非线性性质，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，目标是显着减少电池的使用。该项目中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。这些方程的解的封闭形式的解析表达式是不可用的，因此该系统的理论研究将涉及解析近似和数值计算。 多尺度方法将被用来推导调制方程来描述空间本地化和时间周期性的解决方案，这些近似的误差范围将被探讨。在参数区域中，导出的解析近似是无效的，将采用数值计算。三种情况下的例子被认为是实验实现：粒状晶体，排斥磁铁，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，实施和基准测试。