In recent years, the study of metamaterials has been a subject of much interest, with acoustic metamaterials being applied to a wide range of applications. This utility is in part due to the incorporation of various elements in their design. The addition of local resonators provides greater versatility in controlling vibrations. Nonlinear elements introduce features such as discrete breathers and frequency shift. Electromechanical metamaterials have been established to have great potential for use in simultaneous energy harvesting in addition to vibration control. Furthermore, metamaterials with quasiperiodic patterning have been shown to possess useful properties such as edge-localized modes. However, no works investigate the interaction between all these elements, especially in the nonlinear regime. In this work, we investigate a unique metamaterial with local resonators, nonlinearity, electromechanical elements, and quasiperiodicity. The proposed metamaterial is examined using both analytical and numerical techniques in order to firmly establish the effects of each element.
First, a nonlinear metamaterial with electromechanical local resonators is studied using the perturbation method of multiple scales, wavepacket excitation and direct integration, and specto-spatial processing techniques. The effect of the electromechanical local resonators is established for both the linear and nonlinear regimes, notably including the addition of new bandgaps and pass bands. The influence of electrical parameters on the system dynamics is explored through parametric analysis, demonstrating their use in tuning the system response. It is also shown that nonlinear phenomena such as localized solitons and frequency shift are present in the voltage response of the electromechanical metamaterial.
Next, a nonlinear metamaterial with local resonators and quasiperiodicity is investigated using the method of multiple scales as well as numerical solution of the method of harmonic balance. Topological features stemming from quasiperiodicity are observed in the linear and nonlinear regimes. The presence of local resonators is shown to result in an additional, topologically trivial bandgap. The influence of quasiperiodic parameters and the source of quasiperiodicity on the system's band structure and mode shapes are established in both the linear and nonlinear regimes. Nonlinearity is also shown to affect topological features such as edge modes, resulting in amplitude dependence that can affect the localization of these modes in the nonlinear regime.
Finally, a metamaterial with nonlinearity, electromechanical local resonators, and quasiperiodic patterning is modeled and investigated. Multiple configurations are examined, including different shunt circuits coupled to the electromechanical resonators and different sources of quasiperiodic patterning. It is shown that electromechanical local resonators produce two topologically trivial bandgaps, compared to the single trivial bandgap of the purely mechanical resonator. The influence of mechanical, electrical, and quasiperiodic parameters is explored to establish the effects of these parameters on bandgap formation in the linear regime. The behavior of the metamaterial in the nonlinear regime was found to be consistent with a purely mechanical system, with no adverse effects from the presence of electromechanical elements. The impact of nonlinear and quasiperiodic phenomena on energy harvesting is also investigated. Through exploration of this unique metamaterial, it is shown that beneficial features from all elements can be present at once, resulting in a versatile metamaterial with great potential for numerous applications. / Doctor of Philosophy / In recent years, the study of metamaterials has been a subject of much interest. Despite their name, metamaterials are not homogenous materials, but engineered structures designed to possess properties not found in naturally occurring materials. Many elements can be incorporated into metamaterial design, each with its own benefits. These can range from nonlinear springs, which allow the metamaterial to behave differently as its deformation increases, to electromechanical components, which convert the motion of the metamaterial into electrical voltage. While these elements have been examined individually and in certain combinations, no works examine the combination of elements proposed in this dissertation. In this work, we investigate the impact of nonlinearity, electromechanical components, and two other beneficial elements on the system's vibration response. Combinations of these elements are examined using various analysis techniques, which are used to establish the effects of each element individually as well as their interaction when combined. Multiple variations are examined for each element, such as different types of nonlinearity or different circuits attached to the electromechanical elements. This allows us to confirm the presence of valuable features exclusive to the elements incorporated into the metamaterial. Through exploration of multiple combinations of these metamaterial elements, it is shown that beneficial features from all elements can be present at once, resulting in a versatile metamaterial with great potential for numerous applications.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/120580 |
| Date | 02 July 2024 |
| Creators | Malla, Arun Lee |
| Contributors | Mechanical Engineering, Barry, Oumar, Sarlo, Rodrigo, Zuo, Lei, Sandu, Corina, Taheri, Saied |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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