<p>Metamaterials have gained extensive attention in recent years due to their ability to exhibit material properties otherwise difficult or impossible to obtain using natural materials. Nonlinear and active metamaterials in particular exhibit great promise for exploring new effects and applications, from tunability to mixing. However, nonlinear and active metamaterials have been explored significantly less than linear metamaterials to this point and much work has focused on the fundamental physics of nonlinear metamaterials. Our aim is to further extend the knowledge of practical nonlinear metamaterials and to demonstrate how they can be transformed to real-world applications through the use of embedded devices. In this dissertation, we demonstrate a variety of ways that devices can be embedded within metamaterial unit cells to provide nonlinear and active effects. </p><p>Chapter 1 introduces the basic theory of metamaterials, background of existing work, and the current limitations of nonlinear and active metamaterial design. In Chapter 2, we present the design, simulation, fabrication, and verification of an RF limiter metamaterial. We show how a metamaterial can be designed using RF engineering principles to act as an effective limiter in a new topology, relying on nonlinear devices embedded within a metamaterial. Chapter 3 shows our design and demonstration of a power harvesting metamaterial. We design a nonlinear metamaterial towards a potential application, discussing how the selection of an appropriate embedded device provides our desired functionality. In Chapter 4 we show how nonlinear and active metamaterials can be used to realize phase conjugation, including demonstration of negative refraction and imaging through the use of these metamaterials. We also discuss design approaches to moving these metamaterials towards real-world applications. Chapter 5 discusses our work concerning metamaterials based on transistors. First we show that appropriate design of a transistor circuit allows us to tune the quality factor and resonant frequency of a metamaterial. We use this metamaterial for time-varying mixing, as well, demonstrating a mixing metamaterial that remains linear. We then illustrate how using transistors as nonlinear devices provides much greater design freedom for use with metamaterials. We show that the nonlinearity of a metamaterial can be dramatically enhanced through the use of transistors and even dynamically tuned, applying these nonlinear metamaterials to applications including phase conjugation and acoustoelectromagnetic modulation. In Chapter 6 we summarize the achievements of the presented research and directions for future work that build on the work described in this thesis.</p> / Dissertation

This dissertation investigates the nonlinear wave propagation phenomena in nonlinear metamaterials with nonlinear chains and nonlinear resonators using analytical and spectro-spatial analyses. In the first part of the thesis, the nonlinear metamaterials are modeled as a chain of masses with multiple local resonators attached to each cell. The nonlinearity stems from the chain's stiffness in one case and the local resonator's stiffness in another. Analytical approximates solutions are obtained for each case using perturbation techniques. These results are validated through numerical simulations and the results show good agreement. To further demonstrate the nonlinear wave propagation characteristics, spectro-spatial analyses are conducted on the numerical integration data sets. The wave profiles, short-term Fourier transform spectrograms, and contour plots of 2D Fourier transform show the presence of solitary waves for both sources of nonlinearity. In addition, spectro-spatial features demonstrate the presence of significant frequency shifts at different wavelength limits. indent The second part of the thesis studies a nonlinear electromechanical metamaterial and examines how the electromechanical coupling in the local resonator affects the wave propagation. Numerical examples indicate that the system can be used for simultaneous energy harvesting and vibration attenuation without any degradation in the size of bandgaps. Spectro-spatial analyses conducted on the electromechanical metamaterial also reveal the presence of solitons and frequency shifts. The presence of solitary wave in the electromechanical metamaterial suggests a significant improvement in energy harvesting and sensing techniques. The obtained significant frequency shift is employed to design an electromechanical diode, allowing voltage to be sensed and harvested only in one direction. Design guidelines and the role of different key parameters are presented to help designers to select the type of nonlinearity and the system parameters to improve the performance of acoustic diodes. indent The last part of this thesis studies the passive self-tuning of a metastructure via a beam-sliding mass concept. The governing equations of motions of the holding structure, resonator, and sliding mass are presented and discretized into a system of ODEs using Galerkin's projection. Given that the spatial parameters of the system continuously change over time (i.e., mode shapes and frequencies), instantaneous exact mode shapes and frequencies are determined for all possible slider positions. The numerical integration is conducted by continuously updating the spatial state of the system. The obtained exact mode shapes demonstrate that the resonance frequency of the resonator stretches over a wide frequency band. This observation indicates that the resonator can attenuates vibrations at a wide frequency range. Experiments are also conducted to demonstrate the passive self-tunability of the metastructure and the findings colloborate the analytical results. / Doctor of Philosophy / Metamaterials are artificially engineered structures that can offer incredible dynamical properties, which cannot be found in conventional homogeneous structures. Consequently, the global metamaterials market is expected to display a 23.6$%$ compound annual growth rate through 2027. Some of these exciting properties include, but not limited to, negative stiffness, negative mass, negative Poisson's ratio. The unique dynamic properties show the importance of metamaterials in many engineering applications, such as vibration reduction, noise control, and waveguiding and localization. However, beyond the linear characteristics of metamaterials, nonlinear metamaterials can exhibit more interesting nonlinear wave propagation phenomena, such as solitons, cloaking, tunable bandgaps, and wave non-reciprocity. indent This research work investigates wave propagation characteristics in nonlinear locally resonant metamaterials using analytical, numerical, and signal processing techniques. The nonlinearity stems from the chain in one case and from the local resonator in another. Numerical examples show the presence of solitary waves in both types of nonlinearity and significant frequency shift in certain frequency/wavenumber regions. The obtained significant frequency shift can be utilized to design mechanical diodes, where its operation range can be increased by introducing nonlinearity in the resonator. indent For simultaneous energy harvesting and vibration attenuation, integrating the local resonator with piezoelectric energy harvesters is also investigated in this research work with the presence of both types of nonlinearities. For weak electromechanical coupling, the results demonstrate that the band structure of the system is not affected by the electromechanical coupling. Therefore, the system can also be used for energy harvesting without any degradation in the vibration attenuation performance. This observation is also validated experimentally for the linear limit. Spectro-spatial analyses also reveal the presence of solitary output voltage waves, which can enhance the energy harvesting and sensing. The obtained significant frequency shift can be utilized to design an electromechanical diode where the wave can propagate and be harvested only in one direction. Numerical examples show that the performance of the electromechanical diode can be significantly improved by including nonlinearities in the local resonator. indent Another goal of this research work is the introduction of passive self-tuning mechanism to design self-tuning metastructure. The design of such a metastructure is motivated by the need for broadband devices that can adapt to changing environment. The passive self-tuning concept is achieved by a sliding mass coupled with a resonator. Analytical and experimental results show the ability of this system to tune itself to the excitation frequency, and hence, can control vibrations over a significantly wider frequency band as compared to conventional resonators.

Metamaterials are typically described as materials with ’unusual’ wave propagation properties. Originally developed for electromagnetic waves, these materials have also spread into the field of acoustic wave guiding and cloaking, with the most relevant of these ’unusual’ properties, being the so called band-gap phenomenon. A band-gap signifies a frequency region where elastic waves cannot propagate through the material, which in principle, could be used to protect buildings from earthquakes. Based on this, two relevant concepts have been proposed in the field of seismic engineering, namely: metabarriers, and metamaterial-based foundations. This thesis deals with the development of the Metafoundation, a metamaterial-based foundation system for the seismic protection of fuel storage tanks against excessive base shear and pipeline rupture. Note that storage tanks have proven to be highly sensitive to earthquakes, can trigger sever economic and environmental consequences in case of failure and were therefore chosen as a superstructure for this study. Furthermore, when tanks are protected with traditional base isolation systems, the resulting horizontal displacements, during seismic action, may become excessively large and subsequently damage connected pipelines. A novel system to protect both, tank and pipeline, could significantly augment the overall safety of industrial plants. With the tank as the primary structure of interest in mind, the Metafoundation was conceived as a locally resonant metamaterial with a band gap encompassing the tanks critical eigenfrequency. The initial design comprised a continuous concrete matrix with embedded resonators and rubber inclusions, which was later reinvented to be a column based structure with steel springs for resonator suspension. After investigating the band-gap phenomenon, a parametric study of the system specifications showed that the horizontal stiffness of the overall foundation is crucial to its functionality, while the superstructure turned out to be non-negligible when tuning the resonators. Furthermore, storage tanks are commonly connected to pipeline system, which can be damaged by the interaction between tank and pipeline during seismic events. Due to the complex and nonlinear response of pipeline systems, the coupled tank-pipeline behaviour becomes increasingly difficult to represent through numerical models, which lead to the experimental study of a foundation-tank-pipeline setup. Under the aid of a hybrid simulation, only the pipeline needed to be represented via a physical substructure, while both tank and Metafoundation were modelled as numerical substrucutres and coupled to the pipeline. The results showed that the foundation can effectively reduce the stresses in the tank and, at the same time, limit the displacements imposed on the pipeline. Leading up on this, an optimization algorithm was developed in the frequency domain, under the consideration of superstructure and ground motion spectrum. The advantages of optimizing in the frequency domain were on the one hand the reduction of computational effort, and on the other hand the consideration of the stochastic nature of the earthquake. Based on this, two different performance indices, investigating interstory drifts and energy dissipation, revealed that neither superstructure nor ground motion can be disregarded when designing a metamaterial-based foundation. Moreover, a 4 m tall optimized foundation, designed to remain elastic when verified with a response spectrum analysis at a return period of 2475 years (according to NTC 2018), reduced the tanks base shear on average by 30%. These results indicated that the foundation was feasible and functional in terms of construction practices and dynamic response, yet unpractical from an economic point of view. In order to tackle the issue of reducing the uneconomic system size, a negative stiffness mechanism was invented and implemented into the foundation as a periodic structure. This mechanism, based on a local instability, amplified the metamaterial like properties and thereby enhanced the overall system performance. Note that due to the considered instability, the device exerted a nonlinear force-displacement relationship, which had the interesting effect of reducing the band-gap instead of increasing it. Furthermore, time history analyses demonstrated that with 50% of the maximum admissible negative stiffness, the foundation could be reduced to 1/3 of its original size, while maintaining its performance. Last but not least, a study on wire ropes as resonator suspension was conducted. Their nonlinear behaviour was approximated with the Bouc Wen model, subsequently linearized by means of stochastic techniques and finally optimized with the algorithm developed earlier. The conclusion was that wire ropes could be used as a more realistic suspension mechanism, while maintaining the high damping values required by the optimized foundation layouts. In sum, a metamaterial-based foundation system is developed and studied herein, with the main findings being: (i) a structure of this type is feasible under common construction practices; (ii) the shear stiffness of the system has a fundamental impact on its functionality; (iii) the superstructure cannot be neglected when studying metamaterial-based foundations; (iv) the complete coupled system can be tuned with an optimization algorithm based on calculations in the frequency domain; (v) an experimental study suggests that the system could be advantageous to connected pipelines; (vi) wire ropes may serve as resonator suspension; and (vii) a novel negative stiffness mechanism can effectively improve the system performance.