Nonlinear Elastic Waves in Passive and Active Periodic Media

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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.