Abstract Metamaterials represent a new trend in the field of seismic engineering. Their capacity to attenuate waves at the superstructure level is highly desirable and sought after in recent years. One of their main drawbacks to date, is the excessive size of the necessary resonators and, consequently, the uneconomic design they require. In order to tackle this problem, we apply the concept of negative stiffness to a metamaterial-based foundation system and analyse the potential improvements such a mechanism may have on the metamaterial as well as the coupled structural behaviour. Since negative stiffness is a property that cannot be achieved through conventional measures, a novel mechanism, designed for the implementation in periodic metamaterial-based structures, is proposed herein. The inevitable nonlinearity of the mechanism will be discussed and taken into account, while the advantages of the negative stiffness element (NSE) will be treated analytically and verified numerically. Additionally, through an optimization in the frequency domain and nonlinear time history analyses (THAs), the performance of the system coupled with a fuel storage tank is elaborated. With only 50% of the theoretically allowable NSE value, the foundation system could be reduced to 1/3 of its size. Furthermore, the nonlinear effect of the device has proven to diminish the band gap of the periodic system, which led us to introduce nonlinearity parameters that can help avoid the strongly nonlinear range. In sum, this article tackles three problems that are intertwined: (i) reducing the size of metamaterial-based structures; (ii) the design of a mechanism that exerts a negative stiffness in a periodic structure; and (iii) the study of the inevitable nonlinearity of NSEs and the subsequent effect on the metamaterial behaviour.

中文翻译：

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用非线性负刚度单元增强大型储罐抗震的最优有限局部共振基础

摘要 超材料代表了地震工程领域的新趋势。它们在上层建筑水平上衰减波浪的能力是近年来非常受欢迎和追捧的。迄今为止，它们的主要缺点之一是所需谐振器的尺寸过大，因此它们所需的设计不经济。为了解决这个问题，我们将负刚度的概念应用于基于超材料的基础系统，并分析了这种机制可能对超材料以及耦合结构行为的潜在改进。由于负刚度是一种无法通过常规措施实现的特性，因此本文提出了一种设计用于在基于周期性超材料的结构中实现的新型机制。将讨论和考虑机构不可避免的非线性，同时分析处理负刚度元件 (NSE) 的优点并进行数值验证。此外，通过频域优化和非线性时程分析 (THA)，详细阐述了与燃料储罐耦合的系统性能。只需 50% 的理论允许 NSE 值，基础系统就可以缩小到其尺寸的 1/3。此外，该器件的非线性效应已被证明可以减小周期系统的带隙，这导致我们引入了有助于避免强非线性范围的非线性参数。总之，本文解决了三个相互交织的问题：(i) 减小基于超材料的结构的尺寸；(ii) 在周期性结构中施加负刚度的机构的设计；(iii) 对 NSE 不可避免的非线性及其对超材料行为的后续影响的研究。