## 5 Conclusions  
This study explored the dynamic behavior of metastructures, focusing on those with conventional configurations and those augmented with internally coupled resonators, through a theoretical lens. The development of analytical models deepened our understanding of bandgap dynamics, highlighting the prediction of primary and secondary bandgaps as influenced by internal coupling stiffness. Finite element analysis (FEA) corroborated these theoretical insights, yet it also exposed complexities beyond the analytical models' scope. Insights gained from this study stress the importance of accurately accounting for the physical characteristics of internal couplings and achieving exact stiffness ratios. Additionally, this work shows that adjusting the natural frequencies of resonators through stiffness manipulation--via the strategic positioning of mounted masses--provides a viable approach for customizing vibration isolation solutions. This strategy is particularly relevant for environments subjected to heavy loads and extreme conditions, offering tailored responses to complex vibrational challenges. The principal contributions of this research are as follows:  
* We established a novel transfer function approach for the analysis of metastructures, diverging from traditional bandgap investigation methods such as dispersion analysis and wave finite element methods. * We applied root locus analysis and transfer function modeling, offering new perspectives on metastructure control. * We demonstrated the enhanced dynamic bandgap characteristics achievable through the use of internally coupled resonators, incorporating control engineering techniques for refined metastructure management. This research showcases the fusion of control system theory with metastructure analysis, presenting a groundbreaking approach for the precise manipulation of bandgaps. This methodology not only marks a significant advancement in the understanding and application of vibration control technologies but also opens new avenues for energy-efficient solutions across multiple industries. Specifically, in the automotive sector, the integration of metastructures can significantly reduce noise and vibrations, enhancing vehicle durability. In civil engineering, buildings and infrastructure equipped with optimized bandgaps offer enhanced protection against environmental vibrations and seismic activities. Moreover,  
Figure 12: Binary contour plot of bandgap presence against resonator mass placement (\(\delta\)) and normalized frequency (\(\omega/\omega_{r}\)), with white areas indicating effective vibration isolation regions. the innovative application of these metastructures in energy harvesting from vibrational bandgaps paves the way for smart buildings to achieve superior energy sustainability. Future studies will prioritize empirical validation through experimentation to confirm the theoretical and numerical models' applicability in real-world scenarios. Subsequent research will focus on fabricating metastructures with internally coupled resonators, with a particular emphasis on manufacturing precision to accurately match the stiffness of the resonators, thereby ensuring optimal system performance. Additionally, the integration of piezoelectric materials for vibration suppression and energy harvesting will be explored, aiming to enhance the functional versatility of these advanced materials. The individual contributions of authors to this research article are as follows: Conceptualization, H.A. and K.V. ; methodology, H.A. ; software, H.A. ; validation, H.A., K.V. and S.H.H. ; formal analysis, H.A. ; investigation, H.A. ; resources, S.H.H. ; data curation, K.V. ; writing--original draft preparation, H.A. ; writing--review and editing, K.V. and E.P. ; visualization, S.H.H. ; supervision, S.H.H. ; project administration, E.P. ; funding acquisition, E.P. All authors have read and agreed to the published version of the manuscript. This work was supported by the Estonian Research Council through the grant PRG658. Not applicable.