This study explores the optimization of bandgap characteristics in locally resonant metastructures through advanced artificial intelligence (AI) and optimization algorithms, focusing on the accurate estimation of resonator damping ratios. By developing a novel mathematical framework for metastructure analysis, this research diverges from traditional methods, offering a more nuanced approach to bandgap manipulation. This research significantly improves metastructure modeling accuracy by precisely estimating resonator and structural damping ratios, enhancing model fidelity crucial for analysis, control strategies, and design optimization. Through a combination of model simulations and experimental validation, the efficacy of the Hybrid Genetic Algorithm-Particle Swarm Optimization (GA-PSO) algorithm is demonstrated, highlighting its potential for practical applications in engineering metastructures. This paper not only provides a robust method for estimating damping ratios but also opens new avenues for future research, including the application of machine learning techniques and the development of intelligent materials. The findings of this study contribute to the foundational understanding necessary for the advancement of mathematical modeling metamaterials, with broad implications for industries where precise vibration control is crucial.

Metastructures with internally coupled resonators promise enhanced vibration control and energy harvesting capabilities by theoretically enabling multiple bandgaps. This paper investigates the feasibility of these theoretical benefits under practical constraints, particularly the challenge of merging multiple bandgaps in continuous systems. Employing a closed-form analytical approach alongside FEM simulations and experimental validation, the study reveals that while internal coupling can modify bandgap behavior, achieving precise stiffness alignment and bandgap merging remains challenging. The findings indicate that practical applications may not fully realize the predicted advantages and also present more challenges in merging multiple bandgaps created in such metastructures, even for metastructures with advanced manufacturing precision and design optimization. The paper contributes to the understanding of the dynamic behavior of internally coupled metastructures and outlines directions for future research to bridge the gap between theory and application.