A Positive Effect of Negative Stiffness: Wave Behavior and Energy Management

本研究的目的是分析并利用将负刚度组件纳入机电和结构系统所产生的动态行为。研究重点是带隙、闪烁、双稳、信号放大和频率软化等现象，以及能量耗散和吸收、能量传递、能量收集、波导和吸振器等应用。研究问题包括理解扩展和收缩弹跳状态之间的非线性瞬态动力学，分析和设计低频输入导致的高频动力学，推导负刚度小单元组件的有效动力学特性，开发处理负刚度系统的拓扑优化方法，创新地使用目标函数来设计期望的行为，利用磁弹性基底结构进行实验，以及实验中动态响应的测量和表征。这项研究将结合物理实验和严格的分析技术，如Bloch-Floquet理论和拓扑优化。这项研究支持并导致了新工具的创造，促进了新颖和更有效的工程材料的发展。该作品探索了负刚度元素的概念，以及它们在具有标准材料中不存在的动态特性的组件中的结合。通过使用这些材料而成为可能的先进设备可能会在许多高科技行业中产生增长：医疗诊断设备、无损检测传感设备、汽车、环境（降噪）和能源收集。该研究旨在加强对新兴技术中各种相关现象的理解：周期性介质中的波传播，声学和振动能量管理，声学和超声波范围内的超材料设计。这项工作还为理解负刚度在不同物理领域的影响提供了一个框架，并为利用这种新理解的系统设计提供了新的见解。

The objective of this research is to analyze and then utilize the dynamic behavior that results from incorporating components with negative stiffness into electro-mechanical and structural systems. The research focuses on such phenomena as band-gaps, twinkling, bi-stability, signal magnification and frequency induced softening, towards applications such as energy dissipation and absorption, energy transfer, energy harvesting, waveguides and vibration absorbers. Research issues include understanding of the nonlinear transient dynamics between expanded and contracted snap-through states, analysis and design of high-frequency dynamics that result from low frequency inputs, derivation of effective dynamical properties for assemblies of small scale units of negative stiffness, development of topology optimization methods to handle systems with negative stiffness, innovative usage of objective functions for design of desired behavior, construction of experiments using magneto-elastic base structures, and the measurement and characterization of dynamic responses in experiments. The research will be conducted using a combination of physical experimentation and rigorous analytical techniques, such as Bloch-Floquet theory and topology optimization.This research supports and leads to the creation of new tools that facilitate the development of novel and more effective engineered materials. The work explores the concept of elements of negative stiffness and their incorporation in assemblies that have dynamic properties that do not occur in standard materials. The advanced devices that become possible through the use of these materials are likely to generate growth in a number of high-technology industries: medical diagnostic equipment, sensing devices for non-destructive testing, automotive, environmental (sound abatement), and energy harvesting. The research seeks an enhanced understanding of a variety of phenomena of relevance in emerging technologies: wave propagation in periodic media, acoustic and vibration energy management, metamaterial design in the acoustic and ultrasonic range. The work also provides a framework for the understanding of the effect of negative stiffness in different physical domains and develops new insights into the design of systems that take advantage of this fresh understanding.