Nonlinear Elastic Waves in Passive and Active Periodic Media

被动和主动周期介质中的非线性弹性波结构动力学中的传统观点是将运动幅度保持在尽可能低的水平，以避免触发非线性行为的可能性。因此，机械装置和材料主要是围绕非线性设计的。当人们试图将工程设计的极限推向更雄心勃勃的技术时，这种保守的线性设计观点的影响有限。这是由于线性动态响应机制表现出僵硬和不利的性能特征，例如窄带宽、不能对运行条件的变化做出反应以及不正确的故障(不稳定)预测。拟议研究计划的总体观点是拥抱对非线性的有意利用，以开发具有前所未有的波传播特性的新型机械设备和材料。为此，我们利用周期性弹性介质：晶格材料和机械超材料是由基本构件的周期性重复制成的结构化材料。这些材料的多尺度周期性结构为实现非线性提供了一个自然服从的框架：精心制作的非线性组件可以导致材料动态行为的受控全局变化，如可调动态响应、振动能量局部化、单向波传播和异步运动。这些现象是发现新材料和具有独特功能的结构化系统的关键。拟议的五年计划侧重于两个主要的非线性现象：(I)互惠关系的破裂，(Ii)异步运动的出现。互易性的破坏迫使弹性波沿着相同的传输路径(单向传播)以不同的方向不同地传播。这一特性将指导在屏蔽设备和减震吸收层方面的先进创新的发展。非同步运动是一种非线性行为，材料的不同成分以不同的频率振荡。这种类型的运动将被用来有效地从宽带源中获取机械能。该计划将在理论和实验上确立非线性波传播技术在创造具有高度自适应响应和选择性波控能力的新型晶格材料和机械超材料方面尚未实现的变革潜力。该计划有助于培训加拿大未来学术界和工业界在非线性振动和波传播领域的技术专家。该计划不同阶段产生的知识使几个行业的开创性技术创新成为可能，并对航空航天、汽车和先进材料技术产生关键影响。

Nonlinear Elastic Waves in Passive and Active Periodic Media The conventional wisdom in structural dynamics is to keep the amplitudes of motion as low as possible to avoid the possibility of triggering nonlinear behavior. As a result, mechanical devices and materials are predominantly designed "around" nonlinearity. This conservative linear design perspective has a limited reach when one attempts to push the envelope of engineering design into more ambitious technologies. This is due to the fact that the linear dynamic response regime exhibits rigid and unfavorable performance characteristics such as narrow bandwidth, inability to react to changes in the operating conditions, and incorrect failure (instability) prediction. The overarching perspective of the proposed research program is to embrace the intentional utilization of nonlinearity in order to develop novel mechanical devices and materials that exhibit unprecedented wave propagation characteristics. We take advantage of periodic elastic media for this purpose: lattice materials and mechanical metamaterials are structured materials made from periodic repetitions of a basic building block. The multi-scale periodic structure of these materials provides a naturally amenable framework for implementation of nonlinearity: carefully crafted nonlinear components can lead to controlled global changes in the dynamic behavior of the material such as tunable dynamic response, localization of vibration energy, unidirectional wave propagation and asynchronous motion. These phenomena hold the key to the discovery of new materials and structured systems with unique functionalities. The proposed five-year program is focused on two main nonlinear phenomena: (i) breakdown of reciprocity, (ii) emergence of asynchronous motion. The breakdown of reciprocity enforces elastic waves to travel differently in opposite directions along the same transmission path (unidirectional propagation). This property will guide the development of advanced innovations in shielding devices and absorbing layers for shock and vibration mitigation. Asynchronous motion is a nonlinear behavior in which different components of a material oscillate at different frequencies. This type of motion will be exploited for efficient harvesting of mechanical energy from broadband sources. The proposed program will establish, theoretically and experimentally, the unrealized transformative potential of nonlinear wave propagation technologies in creation of novel lattice materials and mechanical metamaterials with highly adaptive response and selective wave control capabilities. This program contributes to the training of Canada's future technical experts in academia and industry in the field of nonlinear vibrations and wave propagation. The knowledge generated at various stages of this program enables pioneering technological innovations in several industries, with key impact in aerospace, automotive and advanced materials technologies.