DMS-EPSRC: Collaborative Research: Stochastic Dynamics of Vibro-Impact Systems with Applications in Energy Harvesting

电子设备的快速发展，例如集成到物联网中的可穿戴和无线传感器网络，创造了对能够为电池充电以延长其寿命的高效、环保的能量发生器的需求。振动能量收集是一种从自然或强迫振动（如结构运动或人类活动）中收集能量的过程，为这种能量产生提供了一种有前途的手段。这笔赠款利用了数学创新和数据驱动建模之间的协同作用，产生了变革性的工具，用于推进非常有前途但令人惊讶的复杂系统，用于能量收集和有针对性的能量转移。该研究通过支持自充电无线传感器的广泛使用，例如在桥梁，建筑物和离岸可再生能源发电机上，为未来的经济和环境影响做出了贡献。为健康和结构安全监测系统中的无线设备供电将显著降低与有线技术相关的操作和维护成本。因此，对环境的贡献是双重的：作为绿色能源设备的直接贡献，以及通过在可再生能源部门进行有效的诊断和诊断而间接贡献。该补助金的目标是解决数学发展和基于影响的工程设备和系统的实际应用中的差距和机会，这些设备和系统具有非平滑动力学，对于理解振动能量的收获至关重要。该补助金的主要研究目标是开发一套通用的数学方法，用于分析和优化确定性和随机非光滑工程系统的性能。这些方法的重点是追求实际的工程模型的振动冲击能量收集系统和非线性动态阻尼器，有针对性的能量转移的广泛领域。将新的非线性、随机和计算方法与实验和真实世界的数据相结合，用于能量收集和减轻振动的设备，将为基于分析的设计和模型验证铺平新的道路。分析，计算和数据驱动的数学创新之间的协同连接，以推动新的数学方法，并获得设备设计的实际预测。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The rapid development of electronic devices, such as wearable and wireless sensors networks integrated into the Internet of Things, has created the need for efficient, environmentally-friendly energy generators capable of recharging batteries to prolong their lifespan. Vibrational energy harvesting, a process for scavenging energy from natural or forced vibrations such as structural movement or human activity, provides a promising means for this energy generation. This grant leverages a synergy between mathematical innovation and data-driven modeling, yielding transformative tools for advancing highly promising yet surprisingly complex systems for energy harvesting and targeted energy transfer. The research contributes to future economic and environmental impacts by supporting the widespread use of self-recharging wireless sensors, such as on bridges, buildings, and off-shore renewable energy generators. Powering wireless devices in health and structural safety monitoring systems will significantly reduce operation and maintenance costs associated with the wired technologies. The environmental contributions are therefore two-fold: direct, as a green energy device, and indirect through enabling effective diagnostics and prognostics in the renewable energy sector. The goals of this grant address gaps and opportunities in mathematical developments and in practical applications for impact-based engineering devices and systems with non-smooth dynamics, critical for understanding the harvesting of vibrational energy. The main research objective of this grant is to develop a universal suite of mathematical methodologies for the analysis and optimized performance of deterministic and stochastic non-smooth engineering systems. These approaches are pursued with a focus on practical engineering models of vibro-impacting energy harvesting systems and nonlinear dynamic dampers, within the broad area of targeted energy transfer. Integrating novel nonlinear, stochastic, and computational approaches with experimental and real-world data both for energy harvesting and for devices that mitigate vibration will pave new pathways for analysis-based design and model validation. Synergistic connections between analysis, computations and data-driven mathematical innovation are pursued both to drive new mathematical approaches and to obtain practical predictions for device design. This grant will also serve as an excellent cross-disciplinary training ground for the involved postdocs and graduate students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.